View source for Graphene

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{{Short description|Hexagonal lattice made of carbon atoms}}
{{for|the mobile operating system|GrapheneOS}}
{{Not to be confused with|Graphite|Grapheme}}
{{Infobox material
| name                      = Graphene
| image                     = File:Graphen.jpg
| caption                   = Graphene is an [[atomic-scale]] [[Hexagonal lattice|honeycomb structure]] made of [[carbon]] atoms
| type                      = Allotrope of carbon
| chemical formula          = C
| youngs_modulus            = ≈1 TPa
| tensile_strength          = 130 GPa
| thermal_conductivity      = 5300 W⋅m<sup>−1</sup>⋅K<sup>−1</sup>
}}

'''Graphene''' ({{IPAc-en|ˈ|g|r|æ|f|iː|n}})<ref name=camdic/> is a [[carbon allotrope]] consisting of a [[Single-layer materials|single layer]] of [[atom]]s arranged in a [[hexagonal lattice|honeycomb]] planar [[nanostructure]].<ref name="geim2007" /><ref name="peres2009" /> The name "graphene" is derived from "[[graphite]]" and the suffix  [[-ene]], indicating the presence of double bonds within the carbon structure.

Graphene is known for its exceptionally high [[Ultimate tensile strength|tensile strength]], [[Electrical resistivity and conductivity|electrical conductivity]], [[Transparency and translucency|transparency]], and being the thinnest two-dimensional material in the world.<ref>{{Cite news |last=Pike |first=Jared |date=2023 |title=Is graphene the best heat conductor ever? Purdue researchers investigate with four-phonon scattering |url=https://engineering.purdue.edu/ME/News/2023/is-graphene-the-best-heat-conductor-ever-purdue-researchers-investigate-with-fourphonon-scattering |url-status=live |archive-url=https://web.archive.org/web/20240304143824/https://engineering.purdue.edu/ME/News/2023/is-graphene-the-best-heat-conductor-ever-purdue-researchers-investigate-with-fourphonon-scattering |archive-date=March 4, 2024 |access-date=October 1, 2024 |work=Purdue University Mechanical Engineering News}}</ref> Despite the nearly transparent nature of a single graphene sheet, graphite (formed from stacked layers of graphene) appears black because it absorbs all visible light wavelengths.<ref name=nair2008/><ref name=zhu2014/> On a microscopic scale, graphene is the strongest material ever measured.<ref name=lee2008/><ref name=cao2020/>

[[File:Graphene visible.jpg|thumb|Photograph of a suspended graphene membrane in transmitted light. This one-atom-thick material can be seen with the naked eye because it absorbs approximately 2.3% of light.<ref name=zhu2014/><ref name=nair2008/>]]

The existence of graphene was first theorized in 1947 by [[P. R. Wallace|Philip R. Wallace]] during his research on graphite's electronic properties, while the term ''graphene'' was first defined by [[Hanns-Peter Boehm]] in 1987.<ref>{{cite web |title=Graphene: A Complete Chemical History |url=https://www.acsmaterial.com/blog-detail/graphene-a-complete-chemical-history.html |website=ACS Material |access-date=1 October 2024 |date=20 September 2019 |quote=In 1947, the existence of graphene was theorized by Philip R Wallace as an attempt to understand electronic properties of 3D graphite. He did not use the term “graphene”, but instead referred to it as a “single hexagonal layer.” }}</ref> In 2004, the material was isolated and characterized by [[Andre Geim]] and [[Konstantin Novoselov]] at the [[University of Manchester]]<ref name="novo2004" /><ref name="aps2009" /> using a piece of graphite and [[Pressure-sensitive tape|adhesive tape]].<ref>{{Cite web |title=Discovery of graphene - Graphene - The University of Manchester |url=https://www.graphene.manchester.ac.uk/learn/discovery-of-graphene/ |access-date=2024-10-16 |website=www.graphene.manchester.ac.uk}}</ref> In 2010, Geim and Novoselov were awarded the [[Nobel Prize in Physics]] for their "groundbreaking experiments regarding the two-dimensional material graphene".<ref>{{Cite web|title=The Nobel Prize in Physics 2010|url=https://www.nobelprize.org/prizes/physics/2010/summary/|access-date=1 September 2021|publisher=Nobel Foundation|archive-date=22 May 2020|archive-url=https://web.archive.org/web/20200522211920/https://www.nobelprize.org/prizes/physics/2010/summary/|url-status=live}}</ref>  While small amounts of graphene are easy to produce using the method by which it was originally isolated, attempts to scale and automate the manufacturing process for mass production have had limited success due to cost-effectiveness and quality control concerns.<ref>{{Cite web |date=2018-04-06 |title=Mass-Producing Graphene |url=https://www.americanscientist.org/article/mass-producing-graphene |access-date=2024-10-16 |website=American Scientist |language=en}}</ref><ref>{{Cite web |last=Joshi |first=Rita |date=2024-04-08 |title=Can Graphene Be Mass Produced? |url=https://www.azonano.com/article.aspx?ArticleID=6716 |access-date=2024-10-16 |website=AZoNano |language=en}}</ref> The global graphene market was $9 million in 2012,<ref name="azon2014" /> with most of the demand from research and development in [[Semiconductor device|semiconductors]], electronics, [[electric battery|electric batteries]],<ref name="mrmak2014" /> and [[composite material|composites]].

The [[International Union of Pure and Applied Chemistry|IUPAC]] (International Union of Pure and Applied Chemistry) advises using the term "graphite" for the three-dimensional material and reserving "graphene" for discussions about the properties or reactions of single-atom layers.<ref name=IUPAC2009/> A narrower definition, of "isolated or free-standing graphene", requires that the layer be sufficiently isolated from its environment,<ref name=geim2009a/> but would include layers suspended or transferred to [[silicon dioxide]] or [[silicon carbide]].<ref name=ried2009/>

== History ==
{{main|Discovery of graphene}}

[[File:Nobelpriset i fysik 2010.png|thumb|A lump of [[graphite]], a graphene [[transistor]], and a [[tape dispenser]]. Donated to the [[Nobel Museum]] in Stockholm by [[Andre Geim]] and [[Konstantin Novoselov]] in 2010.]]

=== Structure of graphite and its intercalation compounds ===

In 1859, [[Sir Benjamin Collins Brodie, 2nd Baronet|Benjamin Brodie]] noted the highly [[lamella (materials)|lamellar]] structure of thermally reduced [[graphite oxide]].<ref name=geim2012/><ref name=brod1859/> Pioneers in [[X-ray crystallography]] attempted to determine the structure of graphite. The lack of large [[single crystal]] graphite specimens contributed to the independent development of [[powder diffraction|X-ray powder diffraction]] by [[Peter Debye]] and [[Paul Scherrer]] in 1915, and [[Albert Hull]] in 1916.<ref name=deb1916/><ref name=deb1917/><ref name=hull1917/> However, neither of their proposed structures was correct. In 1918, Volkmar Kohlschütter and P. Haenni described the properties of [[graphene oxide paper|graphite oxide paper]].<ref name=kohl1918/> The structure of graphite was successfully determined from single-crystal X-ray diffraction by [[John Bernal|J. D. Bernal]] in 1924,<ref name=bern1924/> although subsequent research has made small modifications to the [[unit cell]] parameters.<ref name=tru1975/><ref name=howe2003/>

The theory of graphene was first explored by [[P. R. Wallace]] in 1947 as a starting point for understanding the electronic properties of 3D graphite. The emergent massless [[Dirac equation]] was separately pointed out in 1984 by [[Gordon Walter Semenoff]],<ref name="Semenoff">{{cite journal |last1=Semenoff |first1=Gordon W. |title=Condensed-Matter Simulation of a Three-Dimensional Anomaly |journal=Physical Review Letters |date=24 December 1984 |volume=53 |issue=26 |pages=2449–2452 |doi=10.1103/PhysRevLett.53.2449 |bibcode=1984PhRvL..53.2449S }}</ref> and by David P. Vincenzo and Eugene J. Mele.<ref name=divi1984/> Semenoff emphasized the occurrence in a magnetic field of an electronic [[Landau level]] precisely at the [[Dirac point]]. This level is responsible for the anomalous integer [[quantum Hall effect]].<ref name=novo2005/><ref name=gusy2005/><ref name=zhang2005/>

=== Observations of thin graphite layers and related structures ===

[[Transmission electron microscopy]] (TEM) images of thin [[graphite]] samples consisting of a few graphene layers were published by G. Ruess and F. Vogt in 1948.<ref name=ruess1948/> Eventually, single layers were also observed directly.<ref name=meyer2007/> Single layers of graphite were also observed by [[transmission electron microscopy]] within bulk materials, particularly inside soot obtained by chemical [[Exfoliation (chemistry)|exfoliation]].<ref name=harris2018/>

From 1961 to 1962, [[Hanns-Peter Boehm]] published a study of extremely thin flakes of graphite.<ref name=boehm1962b/> The study measured flakes as small as ~0.4 [[nanometre|nm]], which is around 3 atomic layers of amorphous carbon. This was the best possible resolution for TEMs in the 1960s. However, it is impossible to distinguish between suspended monolayer and multilayer graphene by their TEM contrasts, and the only known method is to analyze the relative intensities of various diffraction spots.<ref name="meyer2007" /> The first reliable TEM observations of monolayers are likely given in references 24 and 26 of Geim and Novoselov's 2007 review.<ref name=geim2007/>

In 1975, van Bommel et al. [[Epitaxy|epitaxially]] grew a single layer of graphite on top of silicon carbide.<ref name="Bom75">{{cite journal|title=LEED and Auger electron observations of the SiC(0001) surface|year=1975|journal=[[Surface Science (journal)|Surface Science]]|volume=48|pages=463–472|issue=2|last1=van Bommel|first1=A.J.|last2=Crombeen|first2=J.E.|last3=van Tooren|first3=A.|doi=10.1016/0039-6028(75)90419-7|bibcode=1975SurSc..48..463V }}</ref> Others grew single layers of carbon atoms on other materials.<ref name=oshi1997/><ref name=forb1998/> This "epitaxial graphene" consists of a single-atom-thick hexagonal lattice of sp<sup>2</sup>-bonded carbon atoms, as in free-standing graphene. However, there is significant charge transfer between the two materials and, in some cases, hybridization between the [[d-orbital]]s of the substrate atoms and π orbitals of graphene, which significantly alter the electronic structure compared to that of free-standing graphene.

Boehm et al. coined the term "graphene" for the hypothetical single-layer structure in 1986.<ref>{{cite journal|doi=10.1016/0008-6223(86)90126-0|title=Nomenclature and terminology of graphite intercalation compounds|journal=Carbon|volume=24|issue=2|pages=241–245|year=1986|last1=Boehm|first1=H.P|last2=Setton|first2=R|last3=Stumpp|first3=E|bibcode=1986Carbo..24..241B |quote=A single carbon layer of the graphitic structure would be the final member of infinite size of this series. The term ''graphene'' layer should be used for such a single carbon layer.}}</ref> The term was used again in 1987 to describe single sheets of graphite as a constituent of [[graphite intercalation compound]]s,<ref name=mour1987/> which can be seen as crystalline salts of the intercalant and graphene. It was also used in the descriptions of [[carbon nanotube]]s by R. Saito and [[Mildred Dresselhaus|Mildred]] and [[Gene Dresselhaus]] in 1992,<ref name=saito1992/> and in the description of [[Polycyclic aromatic hydrocarbon|polycyclic aromatic hydrocarbons]] in 2000 by S. Wang and others.<ref name=wang2000/>

Efforts to make thin films of graphite by mechanical exfoliation started in 1990.<ref name=geim2008/>
Initial attempts employed exfoliation techniques similar to the drawing method. Multilayer samples down to 10 nm in thickness were obtained.<ref name=geim2007/>

In 2002, Robert B. Rutherford and Richard L. Dudman filed for a patent in the US on a method to produce graphene by repeatedly peeling off layers from a graphite flake adhered to a substrate, achieving a graphite thickness of {{convert|0.00001|inch|mm|abbr=off|lk=on}}. The key to success was the ability to quickly and efficiently identify graphene flakes on the substrate using optical microscopy, which provided a small but visible contrast between the graphene and the substrate.<ref name=ruth2002/>

Another U.S. patent was filed in the same year by Bor Z. Jang and Wen C. Huang for a method to produce graphene-based on exfoliation followed by attrition.<ref name=jang2002/>

In 2014, inventor [[Larry W. Fullerton|Larry Fullerton]] patented a process for producing single-layer graphene sheets.<ref>{{Cite web |title=Graphene edges closer to widespread production and application |url=https://www.compositesworld.com/articles/cedar-ridge-research-receives-pioneer-patent-for-free-floating-graphene-production-technology |access-date=2022-03-25 |website=www.compositesworld.com |date=10 August 2016 |language=en |archive-date=20 September 2020 |archive-url=https://web.archive.org/web/20200920032954/https://www.compositesworld.com/articles/cedar-ridge-research-receives-pioneer-patent-for-free-floating-graphene-production-technology |url-status=live }}</ref>

=== Full isolation and characterization ===
[[File:Nobel Prize 2010-Press Conference KVA-DSC 8009.jpg|thumb|Andre Geim and Konstantin Novoselov at the Nobel Laureate press conference, [[Royal Swedish Academy of Sciences]], 2010.]]

Graphene was properly isolated and characterized in 2004 by [[Andre Geim]] and [[Konstantin Novoselov]] at the [[University of Manchester]].<ref name=novo2004/><ref name=aps2009/> They pulled graphene layers from graphite with a common [[adhesive tape]] in a process called micro-mechanical cleavage, colloquially referred to as the Scotch tape technique.<ref name=manch2014/> The graphene flakes were then transferred onto a thin [[silicon dioxide]] layer on a [[silicon]] plate ("wafer"). The silica electrically isolated the graphene and weakly interacted with it, providing nearly charge-neutral graphene layers. The silicon beneath the {{chem|SiO|2}} could be used as a "back gate" electrode to vary the charge density in the graphene over a wide range.

This work resulted in the two winning the Nobel Prize in Physics in 2010 for their groundbreaking experiments with graphene.<ref name=ukiop2010/><ref name=nobel2013/><ref name=manch2014/> Their publication and the surprisingly easy preparation method that they described, sparked a "graphene gold rush". Research expanded and split off into many different subfields, exploring different exceptional properties of the material—quantum mechanical, electrical, chemical, mechanical, optical, magnetic, etc.

=== Exploring commercial applications ===

Since the early 2000s, several companies and research laboratories have been working to develop commercial applications of graphene. In 2014, a [[National Graphene Institute]] was established with that purpose at the University of Manchester, with a £60&nbsp;million initial funding.<ref name=manch2014f/> In [[North East England]] two commercial manufacturers, Applied Graphene Materials<ref name=burn2014/> and [[Thomas Swan|Thomas Swan Limited]]<ref name=gibs2014/><ref name=thej2014/> have begun manufacturing. [[Cambridge Nanosystems]]<ref name=canew2015/> is a large-scale graphene powder production facility in [[East Anglia]].

== Structure ==
Graphene is a single layer of carbon atoms tightly bound in a hexagonal honeycomb lattice. It is an allotrope of carbon in the form of a plane of sp<sup>2</sup>-bonded atoms with a molecular bond length of {{convert|0.142|nm|angstrom|abbr=on|lk=on}}. In a graphene sheet, each atom is connected to its three nearest carbon neighbors by [[σ-bond]]s, and a delocalized [[π-bond]], which contributes to a [[valence band]] that extends over the whole sheet. This type of [[Bonding in solids|bonding]] is also seen in [[polycyclic aromatic hydrocarbon]]s.<ref name="zdet2015" /><ref name="harris2018" /> The valence band is touched by a [[conduction band]], making graphene a [[semimetal]] with unusual [[electronic properties of graphene|electronic properties]] that are best described by theories for massless relativistic particles.<ref name="geim2007" /> Charge carriers in graphene show linear, rather than quadratic, dependence of energy on momentum, and field-effect transistors with graphene can be made that show bipolar conduction. Charge transport is [[ballistic conduction|ballistic]] over long distances; the material exhibits large [[quantum oscillations]] and large nonlinear [[diamagnetism]].<ref name="lizhi2015" /> 

=== Bonding ===
[[File:Carbon hybrid orbitals - from s+px,py,pz to sp²+pz.svg|thumb|250x250px|Carbon orbitals 2s, 2p<sub>x</sub>, 2p<sub>y</sub> form the hybrid orbital sp<sup>2</sup> with three major lobes at 120°. The remaining orbital, p<sub>z</sub>, extends out of the graphene's plane.]]

[[File:Graphene - sigma and pi bonds.svg|thumb|249x249px|Sigma and pi bonds in graphene. Sigma bonds result from an overlap of sp<sup>2</sup> hybrid orbitals, whereas pi bonds emerge from tunneling between the protruding p<sub>z</sub> orbitals.]]
Three of the four outer-[[electron shell|shell]] [[Electron|electrons]] of each atom in a graphene sheet occupy three sp<sup>2</sup> [[orbital hybridization|hybrid orbitals]] – a combination of orbitals s, p<sub>x</sub> and p<sub>y</sub> — that are shared with the three nearest atoms, forming σ-bonds. The length of these [[carbon–carbon bond|bonds]] is about 0.142 nanometers.<ref name=coop2012/><ref name=felix2013/>

The remaining outer-shell electron occupies a p<sub>z</sub> orbital that is oriented perpendicularly to the plane. These orbitals hybridize together to form two half-filled bands of free-moving electrons, π, and π∗, which are responsible for most of graphene's notable electronic properties.<ref name=coop2012/> Recent quantitative estimates of aromatic stabilization and limiting size derived from the enthalpies of [[hydrogenation]] (ΔH<sub>hydro</sub>) agree well with the literature reports.<ref name=dixit2019/>

Graphene sheets stack to form graphite with an interplanar spacing of {{convert|0.335|nm|angstrom|abbr=on|lk=on}}.<ref>{{Cite book |last=Delhaes |first=Pierre |url=https://books.google.com/books?id=7p2pgNOWPbEC&q=sheet&pg=PA8 |title=Graphite and Precursors |date=2000-12-21 |publisher=CRC Press |isbn=978-90-5699-228-6 |language=en}}</ref>

Graphene sheets in solid form usually show evidence in diffraction for graphite's (002) layering. This is true of some single-walled nanostructures.<ref name=kasu2002/> However, unlayered graphene displaying only (hk0) rings have been observed in the core of [[presolar grains|presolar]] graphite onions.<ref name=bern1996/> TEM studies show faceting at defects in flat graphene sheets<ref name=fraun2002/> and suggest a role for two-dimensional crystallization from a melt.

=== Geometry ===
[[File:Graphene SPM.jpg|thumb|upright|[[Scanning probe microscopy]] image of graphene|alt=]]

The [[Hexagonal lattice|hexagonal lattice structure]] of isolated, single-layer graphene can be directly seen with transmission electron microscopy (TEM) of sheets of graphene suspended between bars of a metallic grid.<ref name=meyer2007/> Some of these images showed a "rippling" of the flat sheet, with an amplitude of about one nanometer. These ripples may be intrinsic to the material as a result of the instability of two-dimensional crystals,<ref name=geim2007/><ref name=carl2007/><ref name=faso2007/> or may originate from the ubiquitous dirt seen in all TEM images of graphene. [[Photoresist]] residue, which must be removed to obtain atomic-resolution images, may be the "[[adsorbate]]s" observed in TEM images, and may explain the observed rippling.<ref>{{Cite journal |last1=Meyer |first1=Jannik C. |last2=Geim |first2=A. K. |last3=Katsnelson |first3=M. I. |last4=Novoselov |first4=K. S. |last5=Booth |first5=T. J. |last6=Roth |first6=S. |date=March 2007 |title=The structure of suspended graphene sheets |url=https://www.nature.com/articles/nature05545 |journal=Nature |language=en |volume=446 |issue=7131 |pages=60–63 |doi=10.1038/nature05545 |pmid=17330039 |arxiv=cond-mat/0701379 |bibcode=2007Natur.446...60M |issn=1476-4687}}</ref>

The hexagonal structure is also seen in [[scanning tunneling microscope]] (STM) images of graphene supported on silicon dioxide substrates<ref name=ishi2007/> The rippling seen in these images is caused by the conformation of graphene to the substrates' lattice and is not intrinsic.<ref name=ishi2007/>

=== Stability ===

[[Ab initio quantum chemistry methods|Ab initio calculations]] show that a graphene sheet is thermodynamically unstable if its size is less than about 20&nbsp;nm and becomes the most stable [[fullerene]] (as within graphite) only for molecules larger than 24,000 atoms.<ref name=shen2006/>

== Electronic properties ==
{{main|Electronic properties of graphene}}
[[File:Electronic band structure of graphene.svg|thumb|306x306px|Electronic band structure of graphene. Valence and conduction bands meet at the six vertices of the hexagonal Brillouin zone and form linearly dispersing Dirac cones.]]
Graphene is a zero-gap [[semiconductor]] because its conduction and [[valence bands]] meet at the [[Dirac cone|Dirac points]]. The Dirac points are six locations in [[momentum space]] on the edge of the [[Brillouin zone]], divided into two non-equivalent sets of three points. These sets are labeled K and K'. These sets give graphene a [[valleytronics|valley degeneracy]] of <math>g_{v} = 2</math>. In contrast, for traditional semiconductors, the primary point of interest is generally Γ, where momentum is zero.<ref name=coop2012/> 

If the in-plane direction is confined rather than infinite, its electronic structure changes. These confined structures are referred to as [[graphene nanoribbon]]s. If the nanoribbon has a "zig-zag" edge, the bandgap remains zero. If it has an "armchair" edge, the bandgap is non-zero.

Graphene's honeycomb structure can be viewed as two interleaving triangular lattices. This perspective has been used to calculate the band structure for a single graphite layer using a tight-binding approximation.<ref name=coop2012/>



=== Electronic spectrum ===

Electrons propagating through the graphene honeycomb lattice effectively lose their mass, producing [[quasi-particle]]s described by a 2D analogue of the [[Dirac equation]] rather than the [[Schrödinger equation]] for spin-{{sfrac|1|2}} particles.<ref name="Castro" /><ref name="E-Phonon">{{cite book |url={{google books |plainurl=yes |id=ammoVEI-H2gC}} |last1=Charlier |first1=J.-C. |last2=Eklund |first2=P.C. |last3=Zhu |first3=J. |last4=Ferrari |first4=A.C. |chapter=Electron and Phonon Properties of Graphene: Their Relationship with Carbon Nanotubes |title=Carbon Nanotubes: Advanced Topics in the Synthesis, Structure, Properties and Applications |editor1-first=A. |editor1-last=Jorio |editor2-first=G. |editor2-last=Dresselhaus |editor3-first=M.S. |editor3-last=Dresselhaus |editor-link3=Mildred Dresselhaus|location=Berlin/Heidelberg |publisher=Springer-Verlag |year=2008|page=673}}</ref>

=== Dispersion relation ===
[[File:Graphene and Dirac Cones.ogv|thumb|Electronic band structure and Dirac cones, with effect of [[doping (semiconductor)|doping]]{{citation needed|date=July 2020}}|220x220px]]

The cleavage technique led directly to the first observation of the anomalous quantum Hall effect in graphene in 2005 by Geim's group and by [[Philip Kim (physicist)|Philip Kim]] and [[Yuanbo Zhang]]. This effect provided direct evidence of graphene's theoretically predicted [[Berry's phase]] of massless [[Dirac fermion]]s and proof of the Dirac fermion nature of electrons.<ref name=novo2005/><ref name=zhang2005/> These effects were previously observed in bulk graphite by Yakov Kopelevich, Igor A. Luk'yanchuk, and others, in 2003–2004.<ref name=kope2003/><ref name=luky2004/>

When atoms are placed onto the graphene hexagonal lattice, the overlap between the ''p''<sub>z</sub>(π) orbitals and the ''s'' or the ''p''<sub>x</sub> and ''p''<sub>y</sub> orbitals is zero by symmetry. Therefore, ''p''<sub>z</sub> electrons forming the π bands in graphene can be treated independently. Within this π-band approximation, using a conventional [[tight-binding]] model, the [[dispersion relation]] (restricted to first-nearest-neighbor interactions only) that produces the energy of the electrons with wave vector ''k'' is:<ref name="Semenoff" /><ref name="Wallace">{{cite journal |last=Wallace |first=P.R. |s2cid=53633968 |title=The Band Theory of Graphite |doi=10.1103/PhysRev.71.622 |journal=Physical Review |volume=71 |year=1947 |pages=622–634 |bibcode=1947PhRv...71..622W |issue=9}}</ref>

:<math>E(k_x,k_y)=\pm\,\gamma_0\sqrt{1+4\cos^2{\tfrac{1}{2}ak_x}+4\cos{\tfrac{1}{2}ak_x} \cdot \cos{\tfrac{\sqrt{3}}{2}ak_y}}</math>

with the nearest-neighbor (π orbitals) hopping energy ''γ''<sub>0</sub> ≈ {{val|2.8 |u=eV}} and the [[lattice constant]] {{nowrap|''a'' ≈ {{val|2.46 |u=Å}}}}. The conduction and valence bands correspond to the different signs. With one ''p''<sub>z</sub> electron per atom in this model, the valence band is fully occupied, while the conduction band is vacant. The two bands touch at the zone corners (the ''K'' point in the Brillouin zone), where there is a zero density of states but no band gap. Thus, graphene exhibits a semi-metallic (or zero-gap semiconductor) character, although this is not true for a graphene sheet rolled into a [[carbon nanotube]] due to its curvature. Two of the six Dirac points are independent, while the rest are equivalent by symmetry. Near the ''K''-points, the energy depends ''linearly'' on the wave vector, similar to a relativistic particle.<ref name="Semenoff"/><ref name="CBE">{{Cite journal |last1=Avouris |first1=P. |last2=Chen |first2=Z. |last3=Perebeinos |first3=V. |title=Carbon-based electronics |doi=10.1038/nnano.2007.300 |journal=Nature Nanotechnology |volume=2 |year=2007 |pmid=18654384 |issue=10 |bibcode=2007NatNa...2..605A |pages=605–15}}</ref> Since an elementary cell of the lattice has a basis of two atoms, the [[wave function]] has an effective [[Spinor|2-spinor structure]].

Consequently, at low energies even neglecting the true spin, electrons can be described by an equation formally equivalent to the massless [[Dirac equation]]. Hence, the electrons and holes are called Dirac [[fermions]].<ref name="Semenoff" /> This pseudo-relativistic description is restricted to the [[Chirality (physics)|chiral limit]], i.e., to vanishing rest mass ''M''<sub>0</sub>, leading to interesting additional features:<ref name="Semenoff" /><ref name="cabra2">{{cite journal |last1=Lamas |first1=C.A. |first2=D.C. |last2=Cabra |first3=N. |last3=Grandi |title=Generalized Pomeranchuk instabilities in graphene |journal=Physical Review B |year=2009 |volume=80 |issue=7 |page=75108 |doi=10.1103/PhysRevB.80.075108 |arxiv=0812.4406 |bibcode=2009PhRvB..80g5108L|s2cid=119213419 }}</ref>

:<math>v_F\, \vec \sigma \cdot \nabla \psi(\mathbf{r})\,=\,E\psi(\mathbf{r}).</math>

Here ''v<sub>F</sub>'' ~ {{val |e=6 |u=m/s}} (.003 c) is the [[Fermi velocity]] in graphene, which replaces the velocity of light in the Dirac theory; <math>\vec{\sigma}</math> is the vector of the [[Pauli matrices]], <math>\psi(\mathbf{r})</math> is the two-component wave function of the electrons, and ''E'' is their energy.<ref name="Castro" />

The equation describing the electrons' linear dispersion relation is:

:<math>E(q)=\hbar v_F q</math>

where the [[wavevector]] ''q'' is measured from the Brillouin zone vertex K, <math>q=\left|\mathbf{k}-\mathrm{K}\right|</math>, and the zero of energy is set to coincide with the Dirac point. The equation uses a pseudospin matrix formula that describes two sublattices of the honeycomb lattice.<ref name="CBE" />

=== Single-atom wave propagation ===

Electron waves in graphene propagate within a single-atom layer, making them sensitive to the proximity of other materials such as [[high-κ dielectric]]s, [[superconductor]]s, and [[ferromagnets]].

=== Ambipolar electron and hole transport ===
[[File:Graphene - Geim - ambipolar FET.svg|thumb|221x221px|When the gate voltage in a field effect graphene device is changed from positive to negative, conduction switches from electrons to holes. The charge carrier concentration is proportional to the applied voltage. Graphene is neutral at zero gate voltage and resistivity is at its maximum because of the dearth of charge carriers. The rapid fall of resistivity when carriers are injected shows their high mobility, here of the order of 5000 cm<sup>2</sup>/Vs. n-Si/SiO<sub>2</sub> substrate, T=1K.<ref name=geim2007/>]]

Graphene exhibits high [[electron mobility]] at room temperature, with values reported in excess of {{val|15000 |u=cm<sup>2</sup>⋅V<sup>−1</sup>⋅s<sup>−1</sup>}}.<ref name=geim2007/> Hole and electron mobilities are nearly identical.<ref name="E-Phonon" /> The mobility is independent of temperature between {{val|10 |u=K}} and {{val|100 |u=K}},<ref name=novo2005/><ref name="GiantMobility">{{cite journal |last1=Morozov |first1=S.V. |last2=Novoselov |first2=K. |last3=Katsnelson |first3=M. |last4=Schedin |first4=F. |last5=Elias |first5=D. |last6=Jaszczak |first6=J. |last7=Geim |first7=A. |title=Giant Intrinsic Carrier Mobilities in Graphene and Its Bilayer |doi=10.1103/PhysRevLett.100.016602 |journal=Physical Review Letters |volume=100 |page=016602 |year=2008 |pmid=18232798 |bibcode=2008PhRvL.100a6602M |issue=1 |arxiv=0710.5304|s2cid=3543049 }}</ref><ref name="E-ph">{{cite journal |last1=Chen |first1=J. H. |last2=Jang |first2=Chaun |last3=Xiao |first3=Shudong |last4=Ishigami |first4=Masa |last5=Fuhrer |first5=Michael S. |title=Intrinsic and Extrinsic Performance Limits of Graphene Devices on {{chem|SiO|2}} |doi=10.1038/nnano.2008.58 |journal=Nature Nanotechnology |volume=3 |year=2008 |pmid=18654504 |issue=4 |pages=206–9|arxiv=0711.3646 |s2cid=12221376 }}</ref> showing minimal change even at room temperature (300 K),<ref name=geim2007/> suggesting that the dominant scattering mechanism is [[defect scattering]]. Scattering by graphene's acoustic [[phonon]]s intrinsically limits room temperature mobility in freestanding graphene to {{val|200000 |u=cm<sup>2</sup>⋅V<sup>−1</sup>⋅s<sup>−1</sup>}} at a carrier density of {{val |e=12 |u=cm<sup>−2</sup>}}.<ref name="E-ph" /><ref name="GrapheneMC">{{cite journal |last1=Akturk |first1=A. |last2=Goldsman |first2=N. |title=Electron transport and full-band electron-phonon interactions in graphene |doi=10.1063/1.2890147 |journal=Journal of Applied Physics |volume=103 |year=2008 |bibcode=2008JAP...103e3702A |issue=5|pages=053702–053702–8 }}</ref>

The corresponding [[resistivity]] of graphene sheets is {{val |e=-8 |u=Ω⋅m}}, lower than the resistivity of [[silver]], which is the lowest known at room temperature.<ref name="UMDnews">[https://newsdesk.umd.edu/scitech/release.cfm?ArticleID=1621 Physicists Show Electrons Can Travel More Than 100 Times Faster in Graphene :: University Communications Newsdesk, University of Maryland] {{webarchive|url=https://web.archive.org/web/20130919083015/https://newsdesk.umd.edu/scitech/release.cfm?ArticleID=1621|date=19 September 2013}}. Newsdesk.umd.edu (24 March 2008). Retrieved on 2014-01-12.</ref> However, on {{chem|SiO|2}} substrates, electron scattering by optical phonons of the substrate has a more significant effect than scattering by graphene's phonons, limiting mobility to {{val|40000 |u=cm<sup>2</sup>⋅V<sup>−1</sup>⋅s<sup>−1</sup>}}.<ref name="E-ph" />

Charge transport can be affected by the adsorption of contaminants such as [[water]] and [[oxygen]] molecules, leading to non-repetitive and large hysteresis I-V characteristics. Researchers need to conduct electrical measurements in a vacuum. Coating the graphene surface with materials such as SiN, [[Poly(methyl methacrylate)|PMMA]] or h-BN has been proposed for protection. In January 2015, the first stable graphene device operation in the air over several weeks was reported for graphene whose surface was protected by [[Aluminium oxide|aluminum oxide]].<ref>{{cite journal |last=Sagade |first=A. A. |s2cid=24846431 |title=Highly Air Stable Passivation of Graphene Based Field Effect Devices |doi=10.1039/c4nr07457b |pmid=25631337 |journal=Nanoscale |volume=7 |issue=8 |pages=3558–3564 |year=2015 |display-authors=etal |bibcode=2015Nanos...7.3558S}}</ref><ref>{{cite web|url=https://spectrum.ieee.org/graphene-devices-stand-the-test-of-time|title=Graphene Devices Stand the Test of Time|date=2015-01-22|access-date=2 February 2020|archive-date=1 August 2020|archive-url=https://web.archive.org/web/20200801055523/https://spectrum.ieee.org/nanoclast/semiconductors/nanotechnology/graphene-devices-stand-the-test-of-time|url-status=live}}</ref> In 2015, [[lithium]]-coated graphene exhibited [[superconductivity]], a first for graphene.<ref>{{cite web |title=Researchers create superconducting graphene |work=Research & Development |url=http://www.rdmag.com/news/2015/09/researchers-create-superconducting-graphene |access-date=2015-09-22 |date=2015-09-09 |archive-date=7 September 2017 |archive-url=https://web.archive.org/web/20170907033306/https://www.rdmag.com/news/2015/09/researchers-create-superconducting-graphene |url-status=live }}</ref>

Electrical resistance in 40-nanometer-wide [[nanoribbon]]s of epitaxial graphene changes in discrete steps. The ribbons' conductance exceeds predictions by a factor of 10. The ribbons can function more like [[optical waveguide]]s or [[quantum dot]]s, allowing electrons to flow smoothly along the ribbon edges. In copper, resistance increases proportionally with length as electrons encounter impurities.<ref name="k1402">{{cite web |url=http://www.kurzweilai.net/new-form-of-graphene-allows-electrons-to-behave-like-photons |title=New form of graphene allows electrons to behave like photons |work=kurzweilai.net |access-date=27 February 2014 |archive-date=2 March 2014 |archive-url=https://web.archive.org/web/20140302070314/http://www.kurzweilai.net/new-form-of-graphene-allows-electrons-to-behave-like-photons? |url-status=live }}</ref><ref name="doi_12952">{{cite journal |doi=10.1038/nature12952 |pmid=24499819 |title=Exceptional ballistic transport in epitaxial graphene nanoribbons |journal=Nature |volume=506 |issue=7488 |pages=349–354 |year=2014 |last1=Baringhaus |first1=J. |last2=Ruan |first2=M. |last3=Edler |first3=F. |last4=Tejeda |first4=A. |last5=Sicot |first5=M. |last6=Taleb-Ibrahimi |first6=A. |last7=Li |first7=A. P. |last8=Jiang |first8=Z. |last9=Conrad |first9=E. H. |last10=Berger |first10=C. |last11=Tegenkamp |first11=C. |last12=De Heer |first12=W. A. |arxiv=1301.5354 |bibcode=2014Natur.506..349B|s2cid=4445858 }}</ref>

Transport is dominated by two modes: one ballistic and temperature-independent, and the other thermally activated. Ballistic electrons resemble those in cylindrical carbon nanotubes. At room temperature, resistance increases abruptly at a specific length—the ballistic mode at 16 micrometers and the thermally activated mode at 160 nanometers (1% of the former length).<ref name="k1402" />

Graphene electrons can traverse micrometer distances without scattering, even at room temperature.<ref name="Castro" />

==== Electrical conductivity and charge transport ====
Despite zero carrier density near the Dirac points, graphene exhibits a minimum conductivity on the order of <math>4e^2/h</math>. The origin of this minimum conductivity is still unclear. However, rippling of the graphene sheet or ionized impurities in the {{chem|SiO|2}} substrate may lead to local puddles of carriers that allow conduction.<ref name="E-Phonon" /> Several theories suggest that the minimum conductivity should be <math>4e^2/{(\pi}h)</math>; however, most measurements are of the order of <math>4e^2/h</math> or greater<ref name="geim2007" /> and depend on impurity concentration.<ref name="K">{{cite journal |last1=Chen |first1=J. H. |last2=Jang |first2=C. |last3=Adam |first3=S. |last4=Fuhrer |first4=M. S. |last5=Williams |first5=E. D. |last6=Ishigami |first6=M. |title=Charged Impurity Scattering in Graphene |doi=10.1038/nphys935 |journal=Nature Physics |volume=4 |pages=377–381 |year=2008 |bibcode=2008NatPh...4..377C |issue=5 |arxiv=0708.2408|s2cid=53419753 }}</ref>

Near zero carrier density, graphene exhibits positive photoconductivity and negative photoconductivity at high carrier density, governed by the interplay between photoinduced changes of both the [[Drude weight]] and the carrier scattering rate.<ref>[http://www.kurzweilai.net/light-pulses-control-how-graphene-conducts-electricity Light pulses control how graphene conducts electricity] {{Webarchive|url=https://web.archive.org/web/20181106192035/http://www.kurzweilai.net/light-pulses-control-how-graphene-conducts-electricity |date=6 November 2018 }}. kurzweilai.net. 4 August 2014</ref>

Graphene doped with various gaseous species (both acceptors and donors) can be returned to an undoped state by gentle heating in a vacuum.<ref name="K" /><ref name="ChemDoping">{{cite journal |last1=Schedin |first1=F. |last2=Geim |first2=A. K. |last3=Morozov |first3=S. V. |last4=Hill |first4=E. W. |last5=Blake |first5=P. |last6=Katsnelson |first6=M. I. |last7=Novoselov |first7=K. S. |title=Detection of individual gas molecules adsorbed on graphene |doi=10.1038/nmat1967 |journal=Nature Materials |volume=6 |pages=652–655 |year=2007 |pmid=17660825 |issue=9 |bibcode=2007NatMa...6..652S|arxiv=cond-mat/0610809 |s2cid=3518448 }}</ref> Even for [[dopant]] concentrations in excess of 10<sup>12</sup> cm<sup>−2</sup>, carrier mobility exhibits no observable change.<ref name="ChemDoping" /> Graphene doped with [[potassium]] in [[ultra-high vacuum]] at low temperature can reduce mobility 20-fold.<ref name="K" /><ref name="GrapheneCharge">{{cite journal |last1=Adam |first1=S. |last2=Hwang |first2=E. H. |last3=Galitski |first3=V. M. |last4=Das Sarma |first4=S. |title=A self-consistent theory for graphene transport |journal=Proc. Natl. Acad. Sci. USA |volume=104 |arxiv=0705.1540 |year=2007 |doi=10.1073/pnas.0704772104 |pmid=18003926 |issue=47 |pmc=2141788 |bibcode=2007PNAS..10418392A |pages=18392–7|doi-access=free }}</ref> The mobility reduction is reversible on heating the graphene to remove the potassium.

Due to graphene's two dimensions, charge fractionalization (where the apparent charge of individual pseudoparticles in low-dimensional systems is less than a single quantum)<ref>{{cite journal |first1=Hadar |last1=Steinberg |first2=Gilad |last2=Barak |first3=Amir |last3=Yacoby |title=Charge fractionalization in quantum wires (Letter) |journal=Nature Physics |volume=4 |issue=2 |year=2008 |pages=116–119 |doi=10.1038/nphys810 |bibcode=2008NatPh...4..116S |arxiv=0803.0744 |s2cid=14581125 |display-authors=etal}}</ref> is thought to occur. It may therefore be a suitable material for constructing [[quantum computer]]s<ref>{{cite journal |arxiv=1003.4590 |title=Dirac four-potential tunings-based quantum transistor utilizing the Lorentz force |first=Agung |last=Trisetyarso |journal=Quantum Information & Computation |url=http://dl.acm.org/citation.cfm?id=2481569.2481576 |volume=12 |year=2012 |page=989 |bibcode=2010arXiv1003.4590T |issue=11–12 |doi=10.26421/QIC12.11-12-7 |s2cid=28441144 |access-date=6 August 2013 |archive-date=6 November 2018 |archive-url=https://web.archive.org/web/20181106210723/https://dl.acm.org/citation.cfm?id=2481569.2481576 |url-status=live }}</ref> using [[anyon]]ic circuits.<ref>{{cite journal |arxiv=0812.1116 |title=Manifestations of topological effects in graphene |first=Jiannis K. |last=Pachos |journal=Contemporary Physics |doi=10.1080/00107510802650507 |volume=50 |year=2009 |pages=375–389 |bibcode=2009ConPh..50..375P |issue=2|s2cid=8825103 }}<br />{{cite web |url=http://www.int.washington.edu/talks/WorkShops/int_08_37W/People/Franz_M/Franz.pdf |title=Fractionalization of charge and statistics in graphene and related structures |first=M. |last=Franz |publisher=University of British Columbia |date=5 January 2008 |access-date=2 September 2009 |archive-date=15 November 2010 |archive-url=https://web.archive.org/web/20101115121039/http://www.int.washington.edu/talks/WorkShops/int_08_37W/People/Franz_M/Franz.pdf |url-status=dead }}</ref>

=== Chiral half-integer quantum Hall effect ===
[[File:Graphene - Geim - Landau levels.svg|thumb|290x290px|Landau levels in graphene appear at energies proportional to √''N'', in contrast to the standard sequence that goes as {{nowrap|''N'' + {{sfrac|1|2}}}}.<ref name=geim2007/>]]

==== Quantum hall effect in graphene ====
The [[quantum Hall effect]] is a quantum mechanical version of the [[Hall effect]], which is the production of transverse (perpendicular to the main current) conductivity in the presence of a [[magnetic field]]. The quantization of the [[Hall effect]] <math>\sigma_{xy}</math> at integer multiples (the "[[Landau level]]") of the basic quantity ''e''<sup>2</sup>/''h'' (where ''e'' is the elementary electric charge and ''h'' is the [[Planck constant]]). It can usually be observed only in very clean [[silicon]] or [[gallium arsenide]] solids at temperatures around {{val|3|ul=K}} and very high magnetic fields.

Graphene shows the quantum Hall effect: the conductivity quantization is unusual in that the sequence of steps is shifted by 1/2 with respect to the standard sequence and with an additional factor of 4. Graphene's Hall conductivity is <math>\sigma_{xy}=\pm {4\cdot\left(N + 1/2 \right)e^2}/h </math>, where ''N'' is the Landau level and the double valley and double spin degeneracies give the factor of 4.<ref name="geim2007" /> These anomalies are present not only at extremely low temperatures but also at room temperature, i.e. at roughly {{convert|20|C|K}}.<ref name="novo2005" />

==== Chiral electrons and anomalies ====
This behavior is a direct result of graphene's chiral, massless Dirac electrons.<ref name="geim2007" /><ref>{{cite journal |last1=Peres |first1=N. M. R. |title=Colloquium : The transport properties of graphene: An introduction |journal=Reviews of Modern Physics |date=15 September 2010 |volume=82 |issue=3 |pages=2673–2700 |doi=10.1103/RevModPhys.82.2673 |arxiv=1007.2849 |bibcode=2010RvMP...82.2673P |s2cid=118585778 }}</ref> In a magnetic field, their spectrum has a Landau level with energy precisely at the Dirac point. This level is a consequence of the [[Atiyah–Singer index theorem]] and is half-filled in neutral graphene,<ref name="Semenoff" /> leading to the "+1/2" in the Hall conductivity.<ref name="gusy2005" /> [[Bilayer graphene]] also shows the quantum Hall effect, but with only one of the two anomalies (i.e. <math>\sigma_{xy}=\pm {4\cdot N\cdot e^2}/h </math>). In the second anomaly, the first plateau at {{nowrap|1=''N'' = 0}} is absent, indicating that bilayer graphene stays metallic at the neutrality point.<ref name="geim2007" />
[[File:Graphene - Geim - Chiral half-integer quantum Hall effect.svg|thumb|220x220px|[[Chirality (chemistry)|Chiral]] half-integer quantum Hall effect in graphene. Plateaux in transverse conductivity appear at half-integer multiples of 4''e''<sup>2</sup>/''h''.<ref name=geim2007/>]]
Unlike normal metals, graphene's longitudinal resistance shows maxima rather than minima for integral values of the Landau filling factor in measurements of the [[Shubnikov–de Haas effect|Shubnikov–de Haas oscillations]], thus the term "''integral'' quantum Hall effect". These oscillations show a phase shift of π, known as [[Geometric phase|Berry's phase]].<ref name=novo2005/><ref name="E-Phonon" /> Berry's phase arises due to chirality or dependence (locking) of the pseudospin quantum number on the momentum of low-energy electrons near the Dirac points.<ref name=zhang2005/> The temperature dependence of the oscillations reveals that the carriers have a non-zero cyclotron mass, despite their zero effective mass in the Dirac-fermion formalism.<ref name=novo2005/>

==== Experimental observations ====
Graphene samples prepared on nickel films, and on both the silicon face and carbon face of [[silicon carbide#Structure and properties|silicon carbide]], show the anomalous effect directly in electrical measurements.<ref name="ByungHeeHong">{{cite journal |last1=Kim |first1=Kuen Soo |title=Large-scale pattern growth of graphene films for stretchable transparent electrodes |year=2009 |doi=10.1038/nature07719 |journal=Nature |volume=457 |pmid=19145232 |issue=7230 |bibcode=2009Natur.457..706K |pages=706–10 |last2=Zhao |first2=Yue |last3=Jang |first3=Houk |last4=Lee |first4=Sang Yoon |last5=Kim |first5=Jong Min |last6=Kim |first6=Kwang S. |last7=Ahn |first7=Jong-Hyun |last8=Kim |first8=Philip |last9=Choi |first9=Jae-Young |last10=Hong |first10=Byung Hee|s2cid=4349731 }}</ref><ref name="0908.1900" /><ref name="ShenAPL" /><ref name="0909.2903" /><ref name="0909.1193" /><ref name="phase1" /> Graphitic layers on the carbon face of silicon carbide show a clear [[Dirac spectrum]] in [[ARPES|angle-resolved photoemission]] experiments, and the effect is observed in cyclotron resonance and tunneling experiments.<ref name="Fuhrer09">{{cite journal |first=Michael S. |last=Fuhrer |title=A physicist peels back the layers of excitement about graphene |doi=10.1038/4591037e |journal=Nature |volume=459 |page=1037 |year=2009 |pmid=19553953 |issue=7250 |bibcode=2009Natur.459.1037F|s2cid=203913300 |doi-access=free }}</ref>

=== "Massive" electrons ===

Graphene's unit cell has two identical carbon atoms and two zero-energy states: one where the electron resides on atom A, and the other on atom B. However, if the unit cell's two atoms are not identical, the situation changes. Research shows that placing [[Boron nitride|hexagonal boron nitride]] (h-BN) in contact with graphene can alter the potential felt at atoms A and B sufficiently for the electrons to develop a mass and an accompanying band gap of about 30 meV.<ref name="sci1306">{{cite journal |last1=Fuhrer |first1=M. S. |year=2013 |title=Critical Mass in Graphene |journal=Science |volume=340 |issue=6139 |pages=1413–1414 |bibcode=2013Sci...340.1413F |doi=10.1126/science.1240317 |pmid=23788788 |s2cid=26403885}}</ref>

The mass can be positive or negative. An arrangement that slightly raises the energy of an electron on atom A relative to atom B gives it a positive mass, while an arrangement that raises the energy of atom B produces a negative electron mass. The two versions behave alike and are indistinguishable via [[optical spectroscopy]]. An electron traveling from a positive-mass region to a negative-mass region must cross an intermediate region where its mass once again becomes zero. This region is gapless and therefore metallic. Metallic modes bounding semiconducting regions of opposite-sign mass is a hallmark of a [[topological phase]] and displays much the same physics as topological insulators.<ref name="sci1306" />

If the mass in graphene can be controlled, electrons can be confined to massless regions by surrounding them with massive regions, allowing the patterning of [[quantum dot]]s, wires, and other mesoscopic structures. It also produces one-dimensional conductors along the boundary. These wires would be protected against [[backscatter]]ing and could carry currents without dissipation.<ref name="sci1306" />

== Interactions and phenomena ==

=== Strong magnetic fields ===

In magnetic fields above 10 [[Tesla (unit)|tesla]], additional plateaus of the Hall conductivity at {{nowrap |1=''σ''<sub>''xy''</sub> = ''νe''<sup>2</sup>/''h''}} with {{nowrap |1=''ν'' = 0, ±1, ±4}} are observed.<ref name="nu-0-1-4">{{cite journal |last1=Zhang |first1=Y. |last2=Jiang |first2=Z. |last3=Small |first3=J. P. |last4=Purewal |first4=M. S. |last5=Tan |first5=Y.-W. |last6=Fazlollahi |first6=M. |last7=Chudow |first7=J. D. |last8=Jaszczak |first8=J. A. |last9=Stormer |first9=H. L. |last10=Kim |first10=P. |title=Landau-Level Splitting in Graphene in High Magnetic Fields |doi=10.1103/PhysRevLett.96.136806 |pmid=16712020 |journal=Physical Review Letters |volume=96 |page=136806 |year=2006 |bibcode=2006PhRvL..96m6806Z |issue=13 |arxiv=cond-mat/0602649|s2cid=16445720 }}</ref> A plateau at {{nowrap |1=''ν'' = 3}}<ref name="nu-3">{{cite journal |last1=Du |first1=X. |last2=Skachko |first2=Ivan |last3=Duerr |first3=Fabian |last4=Luican |first4=Adina |last5=Andrei |first5=Eva Y. |title=Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene |doi=10.1038/nature08522 |journal=Nature |volume=462 |pages=192–195 |year=2009 |issue=7270 |pmid=19829294 |arxiv=0910.2532 |bibcode=2009Natur.462..192D|s2cid=2927627 }}</ref> and the [[fractional quantum Hall effect]] at {{nowrap |1=''ν'' = {{sfrac|1|3}}}} were also reported.<ref name="nu-3" /><ref name="nu-one3rd">{{cite journal |last1=Bolotin |first1=K. |last2=Ghahari |first2=Fereshte |last3=Shulman |first3=Michael D. |last4=Stormer |first4=Horst L. |last5=Kim |first5=Philip |title=Observation of the fractional quantum Hall effect in graphene |doi=10.1038/nature08582 |journal=Nature |volume=462 |pages=196–199 |year=2009 |issue=7270 |pmid=19881489 |arxiv=0910.2763 |bibcode=2009Natur.462..196B|s2cid=4392125 }}</ref> 

These observations with {{nowrap |1=''ν'' = 0, ±1, ±3, ±4}} indicate that the four-fold degeneracy (two valley and two spin degrees of freedom) of the Landau energy levels is partially or completely lifted.

=== Casimir effect ===

The [[Casimir effect]] is an interaction between disjoint neutral bodies provoked by the fluctuations of the electromagnetic vacuum. Mathematically, it can be explained by considering the normal modes of electromagnetic fields, which explicitly depend on the boundary conditions on the interacting bodies' surfaces. Due to graphene's strong interaction with the electromagnetic field as a one-atom-thick material, the Casimir effect has garnered significant interest.<ref name="BFGV">{{cite journal |last1=Bordag |first1=M. |last2=Fialkovsky |first2=I. V. |last3=Gitman |first3=D. M. |last4=Vassilevich |first4=D. V. |title=Casimir interaction between a perfect conductor and graphene described by the Dirac model |journal=Physical Review B |volume=80 |year=2009 |page=245406 |doi=10.1103/PhysRevB.80.245406 |bibcode=2009PhRvB..80x5406B |issue=24 |arxiv=0907.3242|s2cid=118398377 }}</ref><ref name="FMD">{{cite journal |last1=Fialkovsky |first1=I. V. |last2=Marachevsky |first2=V.N. |last3=Vassilevich |first3=D. V. |title=Finite temperature Casimir effect for graphene |year=2011 |volume=84 |issue=35446 |journal=Physical Review B |arxiv=1102.1757 |bibcode=2011PhRvB..84c5446F |page=35446 |doi=10.1103/PhysRevB.84.035446|s2cid=118473227 }}</ref>

=== Van der Waals force ===

The [[Van der Waals force]] (or dispersion force) is also unusual, obeying an inverse cubic asymptotic [[power law]] in contrast to the usual inverse quartic law.<ref name="DWR">{{cite journal |last1=Dobson |first1=J. F. |last2=White |first2=A. |last3=Rubio |first3=A. |title=Asymptotics of the dispersion interaction: analytic benchmarks for van der Waals energy functionals |journal=Physical Review Letters |volume=96 |year=2006 |page=073201 |doi=10.1103/PhysRevLett.96.073201 |pmid=16606085 |issue=7 |bibcode=2006PhRvL..96g3201D |arxiv=cond-mat/0502422|s2cid=31092090 }}</ref>

=== Permittivity ===

Graphene's [[permittivity]] varies with frequency. Over a range from microwave to millimeter wave frequencies, it is approximately 3.3.<ref name="cismaru">{{cite arXiv |last1=Cismaru |first1=Alina |last2=Dragoman |first2=Mircea |last3=Dinescu |first3=Adrian |last4=Dragoman |first4=Daniela |last5=Stavrinidis |first5=G. |last6=Konstantinidis |first6=G. |title=Microwave and Millimeter-wave Electrical Permittivity of Graphene Monolayer |eprint=1309.0990 |year=2013 |class=cond-mat.mes-hall }}</ref> This permittivity, combined with its ability to function as both a conductor and as an insulator, theoretically allows compact [[capacitor]]s made of graphene to store large amounts of electrical energy.

== Optical properties ==
Graphene exhibits unique optical properties, showing unexpectedly high [[Opacity (optics)|opacity]] for an atomic monolayer in vacuum, absorbing approximately {{nowrap|''πα'' ≈ 2.3%}} of [[light]] from visible to infrared wavelengths,<ref name=nair2008/><ref name=zhu2014/><ref>{{cite journal|last1=Kuzmenko|first1=A. B.|last2=Van Heumen|first2=E.|last3=Carbone|first3=F.|last4=Van Der Marel|first4=D.|year=2008|title=Universal infrared conductance of graphite|journal=Physical Review Letters|volume=100|issue=11|page=117401|arxiv=0712.0835|bibcode=2008PhRvL.100k7401K|doi=10.1103/PhysRevLett.100.117401|pmid=18517825|s2cid=17595181}}</ref> where ''α'' is the [[fine-structure constant]]. This is due to the unusual low-energy electronic structure of monolayer graphene, characterized by electron and hole [[conical intersection|conical bands]] meeting at the [[#Electronic properties|Dirac point]], which is qualitatively different from more common quadratic massive bands.<ref name=nair2008/> Based on the Slonczewski–Weiss–McClure (SWMcC) band model of graphite, calculations using [[Fresnel equations]] in the thin-film limit account for interatomic distance, hopping values, and frequency, thus assessing optical conductance.

Experimental verification, though confirmed, lacks the precision required to improve upon existing techniques for determining the [[fine-structure constant]].<ref>{{cite web |title=Graphene Gazing Gives Glimpse Of Foundations Of Universe |url=http://www.sciencedaily.com/releases/2008/04/080403140918.htm |website=ScienceDaily |date=4 April 2008 |access-date=6 April 2008 |archive-date=6 April 2008 |archive-url=https://web.archive.org/web/20080406140754/http://www.sciencedaily.com/releases/2008/04/080403140918.htm |url-status=live }}</ref>

=== Multi-parametric surface plasmon resonance ===
[[Multi-parametric surface plasmon resonance]] has been utilized to characterize both the thickness and refractive index of chemical-vapor-deposition (CVD)-grown graphene films. At a wavelength of {{convert|670|nm|m|abbr=on|lk=on}}, measured refractive index and extinction coefficient values are 3.135 and 0.897, respectively. Thickness determination yielded 3.7 Å across a 0.5mm area, consistent with the 3.35 Å reported for layer-to-layer carbon atom distance of graphite crystals.<ref>{{cite journal |last1=Jussila |first1=Henri |last2=Yang |first2=He |last3=Granqvist |first3=Niko |last4=Sun |first4=Zhipei |title=Surface plasmon resonance for characterization of large-area atomic-layer graphene film |journal=Optica |date=5 February 2016 |volume=3 |issue=2 |pages=151–158 |doi=10.1364/OPTICA.3.000151|bibcode=2016Optic...3..151J |doi-access=free }}</ref> This method is applicable for real-time label-free interactions of graphene with organic and inorganic substances. The existence of unidirectional surface plasmons in nonreciprocal graphene-based gyrotropic interfaces has been theoretically demonstrated, offering tunability from THz to near-infrared and visible frequencies by controlling graphene's chemical potential.<ref>{{cite journal|last1=Lin|first1=Xiao|last2=Xu|first2=Yang |last3=Zhang|first3=Baile|last4=Hao|first4=Ran|last5=Chen|first5=Hongsheng| last6=Li|first6=Erping|title=Unidirectional surface plasmons in nonreciprocal graphene|journal=New Journal of Physics|volume=15|issue=11|page=113003|date=2013|doi=10.1088/1367-2630/15/11/113003|bibcode=2013NJPh...15k3003L|doi-access=free|hdl=10220/17639|hdl-access=free}}</ref> Particularly, the unidirectional frequency bandwidth can be 1– 2 orders of magnitude larger than that achievable with metal under similar magnetic field conditions, stemming from graphene's extremely small effective electron mass.

=== Tunable band gap and optical response ===
Graphene's [[band gap]] can be tuned from 0 to {{val|0.25 |u=eV}} (about 5-micrometer wavelength) by applying a voltage to a dual-gate [[bilayer graphene]] [[field-effect transistor]] (FET) at room temperature.<ref>{{cite journal |doi=10.1038/nature08105 |journal=Nature |last1=Zhang |first1=Y. |last2=Tang |first2=Tsung-Ta |last3=Girit |first3=Caglar |last4=Hao |first4=Zhao |last5=Martin |first5=Michael C. |last6=Zettl |first6=Alex |author6-link=Alex Zettl| last7=Crommie |first7=Michael F. |last8=Shen |first8=Y. Ron |last9=Wang |first9=Feng |volume=459 |pages=820–823 |date=11 June 2009|title=Direct observation of a widely tunable bandgap in bilayer graphene|pmid=19516337|issue=7248 |bibcode=2009Natur.459..820Z |osti=974550 |s2cid=205217165 }}</ref> The optical response of [[graphene nanoribbons]] is tunable into the [[Terahertz radiation|terahertz]] regime by an applied magnetic fields.<ref>{{cite journal |doi=10.1063/1.2964093 |journal=Appl Phys Lett |first1=Junfeng |last1=Liu |first2=A. R. |last2=Wright |first3=Chao |last3=Zhang |first4=Zhongshui |last4=Ma |volume=93 |pages=041106–041110 |date=29 July 2008 |title=Strong terahertz conductance of graphene nanoribbons under a magnetic field |bibcode=2008ApPhL..93d1106L |issue=4 |url=https://ro.uow.edu.au/engpapers/3322 |access-date=30 August 2019 |archive-date=12 June 2020 |archive-url=https://web.archive.org/web/20200612064434/https://ro.uow.edu.au/engpapers/3322/ |url-status=live }}</ref> Graphene/graphene oxide systems exhibit [[electrochromic]] behavior, enabling tuning of both linear and ultrafast optical properties.<ref name="kurum2011" />

=== Graphene-based Bragg grating ===
A graphene-based [[Bragg grating]] (one-dimensional [[photonic crystal]]) has been fabricated, demonstrating its capability to excite surface electromagnetic waves in periodic structure using a {{convert|633|nm|m|abbr=on|lk=on}} He–Ne laser as the light source.<ref>{{cite journal |first1=K.V. |last2=Zeng |first2=Shuwen |last3=Shang |first3=Jingzhi |last4=Yong |first4=Ken-Tye |last5=Yu |first5=Ting |last1=Sreekanth |title=Excitation of surface electromagnetic waves in a graphene-based Bragg grating |journal=Scientific Reports |year=2012 |doi=10.1038/srep00737 |pmid=23071901 |volume=2 |page=737 |bibcode=2012NatSR...2..737S |pmc=3471096}}</ref>

=== Saturable absorption ===

Graphene exhibits unique saturable absorption, which saturates when the input optical intensity exceeds a threshold value. This nonlinear optical behavior, termed [[saturable absorption]], occurs across the visible to [[near-infrared]] spectrum, due to graphene's universal optical absorption and zero band gap. This property has enabled full-band mode-locking in [[fiber laser]]s using graphene-based saturable absorbers, contributing significantly to ultrafast [[photonics]]. Additionally, the optical response of graphene/graphene oxide layers can be electrically tuned.<ref name=kurum2011/><ref name=bao2009/><ref name=zhang2009a/><ref name=zhang2009b/><ref name=zhang2010a/><ref name=zhang2009c/>

Saturable absorption in graphene could occur at the Microwave and Terahertz band, owing to its wideband optical absorption property. The microwave-saturable absorption in graphene demonstrates the possibility of graphene microwaves and terahertz photonics devices, such as a microwave-saturable absorber, modulator, polarizer, microwave signal processing, and broadband wireless access networks.<ref name=zheng2012/>

=== Nonlinear Kerr effect ===

Under intense laser illumination, graphene exhibits a nonlinear phase shift due to the optical nonlinear [[Kerr effect]]. Graphene demonstrates a large nonlinear Kerr coefficient of {{val |e=-7 |u=cm<sup>2</sup>⋅W<sup>−1</sup>}}, nearly nine orders of magnitude larger than that of bulk dielectrics,<ref name="ZHANGHAN">{{cite journal |last1=Zhang |first1=H. |last2=Virally |first2=Stéphane |last3=Bao |first3=Qiaoliang |last4=Kian Ping |first4=Loh |last5=Massar |first5=Serge |last6=Godbout |first6=Nicolas |last7=Kockaert |first7=Pascal |title=Z-scan measurement of the nonlinear refractive index of graphene |journal=Optics Letters |year=2012 |volume=37 |issue=11 |pages=1856–1858 |doi=10.1364/OL.37.001856 |pmid=22660052 |bibcode=2012OptL...37.1856Z|arxiv=1203.5527 |s2cid=119237334 }}</ref> suggesting its potential as a powerful nonlinear Kerr medium capable of supporting various nonlinear effects, including [[soliton|solitons]].<ref>{{cite journal |last1=Dong |first1=H |last2=Conti |first2=C |last3=Marini |first3=A |last4=Biancalana |first4=F |year=2013 |title=Terahertz relativistic spatial solitons in doped graphene metamaterials |journal=Journal of Physics B: Atomic, Molecular and Optical Physics |volume=46 |issue= 15|page=15540|doi=10.1088/0953-4075/46/15/155401 |bibcode=2013JPhB...46o5401D |arxiv=1107.5803 |s2cid=118338133 }}</ref>

== Excitonic properties ==
First-principle calculations incorporating quasiparticle corrections and many-body effects have been employed to study the electronic and optical properties of graphene-based materials. The approach was described as three stages.<ref>{{cite journal |journal=Rev. Mod. Phys. |year=2002 |volume=74 |pages=601–659 |doi=10.1103/RevModPhys.74.601 |bibcode=2002RvMP...74..601O |title=Electronic excitations: Density-functional versus many-body Green's-function approaches |last1=Onida |first1=Giovanni |last2=Rubio |first2=Angel |issue=2 |hdl=10261/98472 |url=https://digital.csic.es/bitstream/10261/98472/1/Electronic%20excitations.pdf |hdl-access=free |access-date=23 September 2019 |archive-date=2 February 2021 |archive-url=https://web.archive.org/web/20210202054314/https://digital.csic.es/bitstream/10261/98472/1/Electronic%20excitations.pdf |url-status=live }}</ref> With GW calculation, the properties of graphene-based materials were accurately investigated, including bulk graphene,<ref>{{cite journal |journal=Physical Review Letters |year=2009 |volume=103 |page=186802 |doi=10.1103/PhysRevLett.103.186802 |bibcode=2009PhRvL.103r6802Y |title=Excitonic Effects on the Optical Response of Graphene and Bilayer Graphene |last1=Yang |first1=Li |last2=Deslippe |first2=Jack |last3=Park |first3=Cheol-Hwan |last4=Cohen |first4=Marvin |last5=Louie |first5=Steven |issue=18 |pmid=19905823 |arxiv=0906.0969|s2cid=36067301 }}</ref> [[graphene nanoribbons|nanoribbons]],<ref>{{cite journal |journal=Physical Review B |year=2008 |volume=77 |page=041404 |doi=10.1103/PhysRevB.77.041404 |title=Optical properties of graphene nanoribbons: The role of many-body effects |last1=Prezzi |first1=Deborah |last2=Varsano |first2=Daniele |last3=Ruini |first3=Alice |last4=Marini |first4=Andrea |last5=Molinari |first5=Elisa |issue=4 |arxiv=0706.0916 |bibcode=2008PhRvB..77d1404P|s2cid=73518107 }}<br />{{cite journal |journal=Nano Letters |year=2007 |volume=7 |pages=3112–5 |doi=10.1021/nl0716404 |title=Excitonic Effects in the Optical Spectra of Graphene Nanoribbons |last1=Yang |first1=Li |last2=Cohen |first2=Marvin L. |last3=Louie |first3=Steven G. |issue=10 |pmid=17824720 |arxiv=0707.2983 |bibcode=2007NanoL...7.3112Y|s2cid=16943236 }}<br />{{cite journal |journal=Physical Review Letters |year=2008 |volume=101 |page=186401 |doi=10.1103/PhysRevLett.101.186401 |bibcode=2008PhRvL.101r6401Y |title=Magnetic Edge-State Excitons in Zigzag Graphene Nanoribbons |last1=Yang |first1=Li |last2=Cohen |first2=Marvin L. |last3=Louie |first3=Steven G. |issue=18 |pmid=18999843}}</ref> edge and surface functionalized armchair ribbons,<ref>{{cite journal |journal=J. Phys. Chem. C |year=2010 |volume=114 |pages=17257–17262 |doi=10.1021/jp102341b |title=Excitons of Edge and Surface Functionalized Graphene Nanoribbons |last1=Zhu |first1=Xi |last2=Su |first2=Haibin |issue=41 |url=https://figshare.com/articles/Excitons_of_Edge_and_Surface_Functionalized_Graphene_Nanoribbons/2719792 |access-date=1 December 2019 |archive-date=1 August 2020 |archive-url=https://web.archive.org/web/20200801070038/https://figshare.com/articles/Excitons_of_Edge_and_Surface_Functionalized_Graphene_Nanoribbons/2719792 |url-status=live }}</ref> hydrogen saturated armchair ribbons,<ref>{{cite journal |journal=Nanoscale |year=2011 |volume=3 |pages=2324–8 |doi=10.1039/c1nr10095e |title=Excitonic properties of hydrogen saturation-edged armchair graphene nanoribbons |last1=Wang |first1=Min |last2=Li |first2=Chang Ming |s2cid=31835103 |issue=5 |pmid=21503364 |bibcode=2011Nanos...3.2324W}}</ref> [[Josephson effect]] in graphene SNS junctions with single localized defect<ref>{{cite journal |first1=Dima |last1=Bolmatov |first2=Chung-Yu |last2=Mou |title=Josephson effect in graphene SNS junction with a single localized defect |journal=Physica B |volume=405 |pages=2896–2899 |year=2010 |doi=10.1016/j.physb.2010.04.015 |issue=13 |arxiv=1006.1391 |bibcode=2010PhyB..405.2896B|s2cid=119226501 }}<br />{{cite journal |first1=Dima |last1=Bolmatov |first2=Chung-Yu |last2=Mou |title=Tunneling conductance of the graphene SNS junction with a single localized defect |journal=Journal of Experimental and Theoretical Physics |volume=110 |pages=613–617 |year=2010 |doi=10.1134/S1063776110040084 |issue=4 |arxiv=1006.1386 |bibcode=2010JETP..110..613B|s2cid=119254414 }}</ref> and armchair ribbon scaling properties.<ref>{{cite journal |title=Scaling of Excitons in Graphene Nanoribbons with Armchair Shaped Edges |journal=Journal of Physical Chemistry A |year=2011 |volume=115 |issue=43 |pages=11998–12003 |doi=10.1021/jp202787h |pmid=21939213 |last1=Zhu |first1=Xi |last2=Su |first2=Haibin |bibcode=2011JPCA..11511998Z |url=https://figshare.com/articles/Scaling_of_Excitons_in_Graphene_Nanoribbons_with_Armchair_Shaped_Edges/2590648 |access-date=1 December 2019 |archive-date=1 August 2020 |archive-url=https://web.archive.org/web/20200801044232/https://figshare.com/articles/Scaling_of_Excitons_in_Graphene_Nanoribbons_with_Armchair_Shaped_Edges/2590648 |url-status=live }}</ref>

=== Spin transport ===

Graphene is considered an ideal material for [[spintronics]] due to its minimal [[spin–orbit interaction]], the near absence of [[nuclear magnetic moment]]s in carbon, and weak [[hyperfine interaction]]. Electrical injection and detection of [[spin current]] have been demonstrated up to room temperature,<ref name="Tombros">{{cite journal |title=Electronic spin transport and spin precession in single graphene layers at room temperature |bibcode=2007Natur.448..571T |last=Tombros |first=Nikolaos |journal=Nature |year=2007 |volume=448 |issue=7153 |pages=571–575 |doi=10.1038/nature06037 |pmid=17632544 |arxiv=0706.1948 |s2cid=4411466 |display-authors=etal}}</ref><ref name="ChoSpin">{{cite journal |first1=Sungjae |last1=Cho |first2=Yung-Fu |last2=Chen |first3=Michael S. |last3=Fuhrer |year=2007 |volume=91 |page=123105 |title=Gate-tunable Graphene Spin Valve |journal=Applied Physics Letters |doi=10.1063/1.2784934 |bibcode=2007ApPhL..91l3105C |issue=12 |arxiv=0706.1597|s2cid=119145153 }}</ref><ref name="Ohishi">{{cite journal |last=Ohishi |first=Megumi |year=2007 |volume=46 |issue=25 |pages=L605–L607 |title=Spin Injection into a Graphene Thin Film at Room Temperature |journal=Jpn J Appl Phys |doi=10.1143/JJAP.46.L605 |bibcode=2007JaJAP..46L.605O |arxiv=0706.1451 |s2cid=119608880 |display-authors=etal}}</ref> with spin coherence length exceeding 1 micrometer observed at this temperature.<ref name="Tombros" /> Control of spin current polarity via electrical gating has been achieved at low temperatures.<ref name="ChoSpin" />

== Magnetic properties ==

=== Strong magnetic fields ===

Graphene's quantum Hall effect in magnetic fields above approximately 10 [[Tesla (unit)|tesla]] reveals additional interesting features. Additional plateaus in Hall conductivity at <math>\sigma_{xy}=\nu e^2/h</math> with <math>\nu=0,\pm {1},\pm {4}</math> have been observed,<ref name="nu-0-1-4" /> along with plateau at <math>\nu=3</math><ref name="nu-3" /> and a fractional quantum Hall effect at <math>\nu=1/3</math>.<ref name="nu-3" /><ref name="nu-one3rd" />

These observations with <math>\nu=0,\pm 1,\pm 3, \pm 4</math> indicate that the four-fold degeneracy (two valley and two spin degrees of freedom) of the Landau energy levels is partially or completely lifted. One hypothesis proposes that [[magnetic catalysis]] of [[symmetry breaking]] is responsible for this degeneracy lift.{{citation needed|date=December 2013}}

=== Spintronic properties ===
Graphene exhibits [[Spintronics|spintronic]] and magnetic properties concurrently.<ref>{{cite journal |last1=Hashimoto |first1=T. |last2=Kamikawa |first2=S. |last3=Yagi |first3=Y. |last4=Haruyama |first4=J. |last5=Yang |first5=H. |last6=Chshiev |first6=M. |title=Graphene edge spins: spintronics and magnetism in graphene nanomeshes |journal=Nanosystems: Physics, Chemistry, Mathematics |date=2014 |volume=5 |issue=1 |pages=25–38 |url=http://nanojournal.ifmo.ru/en/wp-content/uploads/2014/02/NPCM51_P25-38.pdf |access-date=2 May 2019 |archive-date=19 August 2019 |archive-url=https://web.archive.org/web/20190819011954/http://nanojournal.ifmo.ru/en/wp-content/uploads/2014/02/NPCM51_P25-38.pdf |url-status=live }}</ref> Low-defect graphene Nano-meshes, fabricated using a non-lithographic approach, exhibit significant ferromagnetism even at room temperature. Additionally, a spin pumping effect has been observed with fields applied in parallel to the planes of few-layer ferromagnetic nano-meshes, while a [[magnetoresistance]] hysteresis loop is evident under perpendicular fields. Charge-neutral graphene has demonstrated magnetoresistance exceeding 100% in magnetic fields generated by standard permanent magnets (approximately 0.1 tesla), marking a record magneto resistivity ''at room temperature'' among known materials.<ref>{{cite journal |last1=Xin |first1=Na |last2=Lourembam |first2=James |last3=Kumaravadivel |first3=Piranavan |title=Giant magnetoresistance of Dirac plasma in high-mobility graphene |journal=Nature |date=April 2023 |volume=616 |issue=7956 |pages=270–274 |doi=10.1038/s41586-023-05807-0 |pmid=37045919 |pmc=10097601 |arxiv=2302.06863 |bibcode=2023Natur.616..270X }}</ref>

=== Magnetic substrates ===
In 2010 researchers magnetized graphene by producing it via CVD on the Ni(111) substrate<ref>M. Weser, Y. Rehder, K. Horn, M. Sicot, M. Fonin, A. B. Preobrajenski, E. N. Voloshina, E. Goering, and Yu. S. Dedkov, [https://pubs.aip.org/aip/apl/article-abstract/96/1/012504/118906/Induced-magnetism-of-carbon-atoms-at-the-graphene?redirectedFrom=fulltext "Induced magnetism of carbon atoms at the graphene/Ni(111) interface"]</ref> and then in 2014 by placing it on an atomically smooth layer of magnetic [[yttrium iron garnet]], maintaining graphene's electronic properties unaffected. Previous methods involved doping graphene with other substances.<ref>T. Hashimoto, S. Kamikawa, Y. Yagi, J. Haruyama, H. Yang, M. Chshiev, [http://nanojournal.ifmo.ru/en/articles-2/volume5/5-1/paper02/ "Graphene edge spins: spintronics and magnetism in graphene nanomeshes"] {{Webarchive|url=https://web.archive.org/web/20190505085205/http://nanojournal.ifmo.ru/en/articles-2/volume5/5-1/paper02/ |date=5 May 2019 }}, February 2014, Volume 5, Issue 1, pp 25</ref> The dopant's presence negatively affected its electronic properties.<ref>{{cite news |url=http://www.gizmag.com/magnetized-graphene/35805 |title=Scientists give graphene one more quality – magnetism |first=Ben |last=Coxworth |date=January 27, 2015 |access-date=6 October 2016 |publisher=Gizmag |archive-date=14 July 2016 |archive-url=https://web.archive.org/web/20160714203936/http://www.gizmag.com/magnetized-graphene/35805/? |url-status=live }}</ref>

== Mechanical properties ==
The (two-dimensional) density of graphene is 0.763&nbsp;mg per square meter.{{citation needed|date=July 2020}}

Graphene is the strongest material ever tested,<ref name="lee2008" /><ref name="cao2020" /> with an intrinsic [[tensile strength]] of {{convert|130|GPa|abbr=on|lk=on}} (with representative engineering tensile strength ~50-60 GPa for stretching large-area freestanding graphene) and a [[Young's modulus]] (stiffness) close to {{convert|1|TPa|abbr=on|lk=on}}. The Nobel announcement illustrated this by saying that a 1 square meter graphene hammock would support a {{val|4 |u=kg}} cat but would weigh only as much as one of the cat's whiskers, at {{val|0.77 |u=mg}} (about 0.001% of the weight of {{val|1 |u=m<sup>2</sup>}} of paper).<ref name="nobelprize.org">{{cite web |url=http://www.nobelprize.org/nobel_prizes/physics/laureates/2010/advanced-physicsprize2010.pdf |title=Scientific Background on the Nobel Prize in Physics 2010 GRAPHENE |publisher=Nobel Prize |date=5 October 2010 |author=Class for Physics of the Royal Swedish Academy of Sciences |url-status=dead |archive-url= https://web.archive.org/web/20180701222510/https://www.nobelprize.org/nobel_prizes/physics/laureates/2010/advanced-physicsprize2010.pdf |archive-date= Jul 1, 2018 }}</ref>

Large-angle bending of graphene monolayers with minimal strain demonstrates its mechanical robustness. Even under extreme deformation, monolayer graphene maintains excellent carrier mobility.<ref>{{cite journal|last1=Briggs|first1=Benjamin D.|last2=Nagabhirava|first2=Bhaskar|last3=Rao|first3=Gayathri|last4=Deer|first4=Robert|last5=Gao|first5=Haiyuan|last6=Xu|first6=Yang|last7=Yu|first7=Bin|title=Electromechanical robustness of monolayer graphene with extreme bending|journal=Applied Physics Letters |volume=97|issue=22|page=223102|date=2010|doi=10.1063/1.3519982|bibcode=2010ApPhL..97v3102B}}</ref>

The [[spring constant]] of suspended graphene sheets has been measured using an [[atomic force microscope]] (AFM). Graphene sheets were suspended over {{chem|SiO|2}} cavities where an AFM tip was used to apply stress to the sheet to test its mechanical properties. Its spring constant was in the range 1–5&nbsp; N/m and the stiffness was {{val|0.5 |u=TPa}}, which differs from that of bulk graphite. These intrinsic properties could lead to applications such as [[Nanoelectromechanical systems|NEMS]] as pressure sensors and resonators.<ref>{{cite journal |last1=Frank |first1=I. W. |last2=Tanenbaum |first2=D. M. |last3=Van Der Zande |first3=A.M. |last4=McEuen |first4=P. L. |title=Mechanical properties of suspended graphene sheets |doi=10.1116/1.2789446 |journal=Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures |volume=25 |pages=2558–2561 |year=2007 |url=http://www.lassp.cornell.edu/lassp_data/mceuen/homepage/Publications/JVSTB_Pushing_Graphene.pdf |bibcode=2007JVSTB..25.2558F |issue=6 |access-date=21 April 2009 |archive-date=11 July 2009 |archive-url=https://web.archive.org/web/20090711105102/http://www.lassp.cornell.edu/lassp_data/mceuen/homepage/Publications/JVSTB_Pushing_Graphene.pdf |url-status=live }}</ref> Due to its large surface energy and out of plane ductility, flat graphene sheets are unstable with respect to scrolling, i.e. bending into a cylindrical shape, which is its lower-energy state.<ref name="nmscrolling">{{cite journal |first1=S. |last1=Braga |first2=V. R. |last2=Coluci |first3=S. B. |last3=Legoas |first4=R. |last4=Giro |first5=D. S. |last5=Galvão |first6=R. H. |last6=Baughman |year=2004 |title=Structure and Dynamics of Carbon Nanoscrolls |journal=Nano Letters |volume=4 |pages=881–884 |doi=10.1021/nl0497272 |bibcode=2004NanoL...4..881B |issue=5}}</ref>

In two-dimensional structures like graphene, thermal and quantum fluctuations cause relative displacement, with fluctuations growing logarithmically with structure size as per the [[Mermin–Wagner theorem]]. This shows that the amplitude of long-wavelength fluctuations grows logarithmically with the scale of a 2D structure, and would therefore be unbounded in structures of infinite size. Local deformation and elastic strain are negligibly affected by this long-range divergence in relative displacement. It is believed that a sufficiently large 2D structure, in the absence of applied lateral tension, will bend and crumple to form a fluctuating 3D structure. Researchers have observed ripples in suspended layers of graphene,<ref name="meyer2007" /> and it has been proposed that the ripples are caused by thermal fluctuations in the material. As a consequence of these dynamical deformations, it is debatable whether graphene is truly a 2D structure.<ref name="geim2007" /><ref name="carl2007" /><ref name="faso2007" /><ref name="bolm2011a" /><ref name="bolm2011b" /> These ripples, when amplified by vacancy defects, induce a negative [[Poisson's ratio]] into graphene, resulting in the thinnest [[auxetics|auxetic]] material known so far.<ref name="grima2014" />

Graphene-nickel (Ni) composites, created through plating processes, exhibit enhanced mechanical properties due to strong Ni-graphene interactions inhibiting dislocation sliding in the Ni matrix.<ref>{{cite journal|last1=Ren|first1=Zhaodi|last2=Meng|first2=Nan|last3=Shehzad|first3=Khurram|last4=Xu|first4=Yang|last5=Qu|first5=Shaoxing|last6=Yu|first6=Bin|last7=Luo|first7=Jack|title=Mechanical properties of nickel-graphene composites synthesized by electrochemical deposition|journal=Nanotechnology|volume=26|issue=6|page=065706|date=2015|doi=10.1088/0957-4484/26/6/065706|pmid=25605375|bibcode=2015Nanot..26f5706R|s2cid=9501340 |url=http://ubir.bolton.ac.uk/1575/1/Mechanical%20properties%20of%20nickel-graphene%20composites%20synthesized%20by%20electrochemical%20deposition.pdf|access-date=7 January 2020|archive-date=27 October 2020|archive-url=https://web.archive.org/web/20201027171300/http://ubir.bolton.ac.uk/1575/1/Mechanical%20properties%20of%20nickel-graphene%20composites%20synthesized%20by%20electrochemical%20deposition.pdf|url-status=dead}}</ref>

=== Fracture toughness ===

In 2014, researchers from [[Rice University]] and the [[Georgia Institute of Technology]] have indicated that despite its strength, graphene is also relatively [[brittle]], with a [[fracture toughness]] of about 4 MPa√m.<ref name="ZhangMa2014">{{cite journal |last1=Zhang |first1=Peng |last2=Ma |first2=Lulu |last3=Fan |first3=Feifei |last4=Zeng |first4=Zhi |last5=Peng |first5=Cheng |last6=Loya |first6=Phillip E. |last7=Liu |first7=Zheng |last8=Gong |first8=Yongji |last9=Zhang |first9=Jiangnan |last10=Zhang |first10=Xingxiang |last11=Ajayan |first11=Pulickel M. |last12=Zhu |first12=Ting |last13=Lou |first13=Jun |title=Fracture toughness of graphene |journal=Nature Communications |volume=5 |page=3782 |year=2014 |doi=10.1038/ncomms4782 |pmid=24777167 |bibcode=2014NatCo...5.3782Z |doi-access=free }}</ref> This indicates that imperfect graphene is likely to crack in a brittle manner like [[Ceramic#Mechanical properties|ceramic materials]], as opposed to many [[Metal#Form and structure|metallic materials]] which tend to have fracture toughness in the range of 15–50&nbsp;MPa√m. Later in 2014, the Rice team announced that graphene showed a greater ability to distribute force from an impact than any known material, ten times that of steel per unit weight.<ref>{{Cite news |url=http://singularityhub.com/2014/12/04/graphene-armor-would-be-light-flexible-and-far-stronger-than-steel/ |title=Graphene Armor Would Be Light, Flexible and Far Stronger Than Steel |last=Dorrieron |first=Jason |date=4 December 2014 |work=Singularity Hub |access-date=6 October 2016 |archive-date=30 August 2016 |archive-url=https://web.archive.org/web/20160830142957/http://singularityhub.com/2014/12/04/graphene-armor-would-be-light-flexible-and-far-stronger-than-steel/ |url-status=live }}</ref> The force was transmitted at {{convert|22.2|km/s}}.<ref>{{cite news |url=http://www.gizmag.com/graphene-bulletproof-armor/35004 |title=Graphene could find use in lightweight ballistic body armor |first=Ben |last=Coxworth |date=1 December 2014 |work=Gizmag |access-date=6 October 2016 |archive-date=23 July 2016 |archive-url=https://web.archive.org/web/20160723233608/http://www.gizmag.com/graphene-bulletproof-armor/35004/ |url-status=live }}</ref>

=== Polycrystalline graphene ===

Various methods – most notably, [[chemical vapor deposition]] (CVD), as discussed in the section below – have been developed to produce large-scale graphene needed for device applications. Such methods often synthesize polycrystalline graphene.<ref name=":5">{{cite journal |last1=Papageorgiou |first1=Dimitrios G. |last2=Kinloch |first2=Ian A. |last3=Young |first3=Robert J. |title=Mechanical properties of graphene and graphene-based nanocomposites |journal=Progress in Materials Science |date=October 2017 |volume=90 |pages=75–127 |doi=10.1016/j.pmatsci.2017.07.004 |doi-access=free }}</ref> The mechanical properties of polycrystalline graphene are affected by the nature of the defects, such as [[Grain boundary|grain-boundaries (GB)]] and [[Vacancy defect|vacancies]], present in the system and the average grain-size.

Graphene grain boundaries typically contain heptagon-pentagon pairs. The arrangement of such defects depends on whether the GB is in a zig-zag or armchair direction. It further depends on the tilt-angle of the GB.<ref>{{cite journal |last1=Li |first1=J.C.M. |title=Disclination model of high angle grain boundaries |journal=Surface Science |date=June 1972 |volume=31 |pages=12–26 |doi=10.1016/0039-6028(72)90251-8 |bibcode=1972SurSc..31...12L }}</ref> In 2010, researchers from [[Brown University]] computationally predicted that as the tilt-angle increases, the grain boundary strength also increases. They showed that the weakest link in the grain boundary is at the critical bonds of the heptagon rings. As the grain boundary angle increases, the strain in these heptagon rings decreases, causing the grain boundary to be stronger than lower-angle GBs. They proposed that, in fact, for sufficiently large angle GB, the strength of the GB is similar to pristine graphene.<ref>{{cite journal |last1=Grantab |first1=R. |last2=Shenoy |first2=V. B. |last3=Ruoff |first3=R. S. |title=Anomalous Strength Characteristics of Tilt Grain Boundaries in Graphene |journal=Science |date=12 November 2010 |volume=330 |issue=6006 |pages=946–948 |doi=10.1126/science.1196893 |pmid=21071664 |bibcode=2010Sci...330..946G |arxiv=1007.4985 |s2cid=12301209 }}</ref> In 2012, it was further shown that the strength can increase or decrease, depending on the detailed arrangements of the defects.<ref>{{cite journal |last1=Wei |first1=Yujie |last2=Wu |first2=Jiangtao |last3=Yin |first3=Hanqing |last4=Shi |first4=Xinghua |last5=Yang |first5=Ronggui |last6=Dresselhaus |first6=Mildred |title=The nature of strength enhancement and weakening by pentagon–heptagon defects in graphene |journal=Nature Materials |date=September 2012 |volume=11 |issue=9 |pages=759–763 |doi=10.1038/nmat3370 |pmid=22751178 |bibcode=2012NatMa..11..759W |url=http://dspace.imech.ac.cn/handle/311007/46051 |access-date=30 August 2019 |archive-date=22 November 2019 |archive-url=https://web.archive.org/web/20191122205832/http://dspace.imech.ac.cn/handle/311007/46051 |url-status=live }}</ref> These predictions have since been supported by experimental evidence. In a 2013 study led by James Hone's group, researchers probed the elastic [[stiffness]] and [[Strength of materials|strength]] of CVD-grown graphene by combining nano-indentation and high-resolution [[Transmission electron microscopy|TEM]]. They found that the elastic stiffness is identical and strength is only slightly lower than those in pristine graphene.<ref>{{cite journal |last1=Lee |first1=G.-H. |last2=Cooper |first2=R. C. |last3=An |first3=S. J. |last4=Lee |first4=S. |last5=van der Zande |first5=A. |last6=Petrone |first6=N. |last7=Hammerberg |first7=A. G. |last8=Lee |first8=C. |last9=Crawford |first9=B. |last10=Oliver |first10=W. |last11=Kysar |first11=J. W. |last12=Hone |first12=J. |title=High-Strength Chemical-Vapor-Deposited Graphene and Grain Boundaries |journal=Science |date=31 May 2013 |volume=340 |issue=6136 |pages=1073–1076 |doi=10.1126/science.1235126 |pmid=23723231 |bibcode=2013Sci...340.1073L |s2cid=35277622 }}</ref> In the same year, researchers from [[University of California, Berkeley]] and [[University of California, Los Angeles]] probed bi-crystalline graphene with [[Transmission electron microscopy|TEM]] and [[Atomic force microscopy|AFM]]. They found that the strength of grain boundaries indeed tends to increase with the tilt angle.<ref>{{cite journal |last1=Rasool |first1=Haider I. |last2=Ophus |first2=Colin |last3=Klug |first3=William S. |last4=Zettl |first4=A. |last5=Gimzewski |first5=James K. |title=Measurement of the intrinsic strength of crystalline and polycrystalline graphene |journal=Nature Communications |date=December 2013 |volume=4 |issue=1 |page=2811 |doi=10.1038/ncomms3811 |bibcode=2013NatCo...4.2811R |doi-access=free }}</ref>

While the presence of vacancies is not only prevalent in polycrystalline graphene, vacancies can have significant effects on the strength of graphene. The consensus is that the strength decreases along with increasing densities of vacancies. Various studies have shown that for graphene with a sufficiently low density of vacancies, the strength does not vary significantly from that of pristine graphene. On the other hand, a high density of vacancies can severely reduce the strength of graphene.<ref name=":7">{{cite journal |last1=Zhang |first1=Teng |last2=Li |first2=Xiaoyan |last3=Gao |first3=Huajian |title=Fracture of graphene: a review |journal=International Journal of Fracture |date=November 2015 |volume=196 |issue=1–2 |pages=1–31 |doi=10.1007/s10704-015-0039-9 |s2cid=135899138 }}</ref>

Compared to the fairly well-understood nature of the effect that grain boundary and vacancies have on the mechanical properties of graphene, there is no clear consensus on the general effect that the average grain size has on the strength of polycrystalline graphene.<ref name=":6">{{cite journal |last1=Akinwande |first1=Deji |last2=Brennan |first2=Christopher J. |last3=Bunch |first3=J. Scott |last4=Egberts |first4=Philip |last5=Felts |first5=Jonathan R. |last6=Gao |first6=Huajian |last7=Huang |first7=Rui |last8=Kim |first8=Joon-Seok |last9=Li |first9=Teng |last10=Li |first10=Yao |last11=Liechti |first11=Kenneth M. |last12=Lu |first12=Nanshu |last13=Park |first13=Harold S. |last14=Reed |first14=Evan J. |last15=Wang |first15=Peng |last16=Yakobson |first16=Boris I. |last17=Zhang |first17=Teng |last18=Zhang |first18=Yong-Wei |last19=Zhou |first19=Yao |last20=Zhu |first20=Yong |title=A review on mechanics and mechanical properties of 2D materials—Graphene and beyond |journal=Extreme Mechanics Letters |date=May 2017 |volume=13 |pages=42–77 |doi=10.1016/j.eml.2017.01.008 |arxiv=1611.01555 |bibcode=2017ExML...13...42A |s2cid=286118 }}</ref><ref name=":7" /><ref name=":8">{{cite journal |last1=Isacsson |first1=Andreas |last2=Cummings |first2=Aron W |last3=Colombo |first3=Luciano |last4=Colombo |first4=Luigi |last5=Kinaret |first5=Jari M |last6=Roche |first6=Stephan |title=Scaling properties of polycrystalline graphene: a review |journal=2D Materials |date=19 December 2016 |volume=4 |issue=1 |page=012002 |doi=10.1088/2053-1583/aa5147 |arxiv=1612.01727 |s2cid=118840850 }}</ref> In fact, three notable theoretical or computational studies on this topic have led to three different conclusions.<ref name=":9">{{Cite journal|last1=Kotakoski|first1=Jani|last2=Meyer|first2=Jannik C.|date=2012-05-24|title=Mechanical properties of polycrystalline graphene based on a realistic atomistic model|journal=Physical Review B|volume=85|issue=19|page=195447|doi=10.1103/PhysRevB.85.195447|bibcode=2012PhRvB..85s5447K|arxiv=1203.4196|s2cid=118835225}}</ref><ref name=":10">{{cite journal |last1=Song |first1=Zhigong |last2=Artyukhov |first2=Vasilii I. |last3=Yakobson |first3=Boris I. |last4=Xu |first4=Zhiping |title=Pseudo Hall–Petch Strength Reduction in Polycrystalline Graphene |journal=Nano Letters |date=10 April 2013 |volume=13 |issue=4 |pages=1829–1833 |doi=10.1021/nl400542n |pmid=23528068 |bibcode=2013NanoL..13.1829S }}</ref><ref name=":11">{{cite journal |last1=Sha |first1=Z. D. |last2=Quek |first2=S. S. |last3=Pei |first3=Q. X. |last4=Liu |first4=Z. S. |last5=Wang |first5=T. J. |last6=Shenoy |first6=V. B. |last7=Zhang |first7=Y. W. |title=Inverse Pseudo Hall-Petch Relation in Polycrystalline Graphene |journal=Scientific Reports |date=May 2015 |volume=4 |issue=1 |page=5991 |doi=10.1038/srep05991 |pmid=25103818 |pmc=4125985 |bibcode=2014NatSR...4.5991S }}</ref> First, in 2012, Kolakowski and Myer studied the mechanical properties of polycrystalline graphene with "realistic atomistic model", using [[Molecular dynamics|molecular-dynamics]] (MD) simulation. To emulate the growth mechanism of CVD, they first randomly selected [[nucleation]] sites that are at least 5A (arbitrarily chosen) apart from other sites. Polycrystalline graphene was generated from these nucleation sites and was subsequently annealed at 3000K, and then quenched. Based on this model, they found that cracks are initiated at grain-boundary junctions, but the grain size does not significantly affect the strength.<ref name=":9" /> Second, in 2013, Z. Song et al. used MD simulations to study the mechanical properties of polycrystalline graphene with uniform-sized hexagon-shaped grains. The hexagon grains were oriented in various lattice directions and the GBs consisted of only heptagon, pentagon, and hexagonal carbon rings. The motivation behind such a model was that similar systems had been experimentally observed in graphene flakes grown on the surface of liquid copper. While they also noted that crack is typically initiated at the triple junctions, they found that as the grain size decreases, the yield strength of graphene increases. Based on this finding, they proposed that polycrystalline follows pseudo [[Hall-Petch relationship]].<ref name=":10" /> Third, in 2013, Z. D. Sha et al. studied the effect of grain size on the properties of polycrystalline graphene, by modeling the grain patches using [[Voronoi diagram|Voronoi construction]]. The GBs in this model consisted of heptagons, pentagons, and hexagons, as well as squares, octagons, and vacancies. Through MD simulation, contrary to the aforementioned study, they found an inverse Hall-Petch relationship, where the strength of graphene increases as the grain size increases.<ref name=":11" /> Experimental observations and other theoretical predictions also gave differing conclusions, similar to the three given above.<ref name=":8" /> Such discrepancies show the complexity of the effects that grain size, arrangements of defects, and the nature of defects have on the mechanical properties of polycrystalline graphene.

== Other properties ==

=== Thermal conductivity ===

Thermal transport in graphene is a burgeoning area of research, particularly for its potential applications in thermal management. Most experimental measurements have posted large uncertainties in the results of thermal conductivity due to the limitations of the instruments used. Following predictions for graphene and related [[carbon nanotubes]],<ref name="DT130">{{cite journal |last1=Berber |first1=Savas |last2=Kwon |first2=Young-Kyun |last3=Tománek |first3=David |author-link3=David Tománek |date=2000 |title=Unusually High Thermal Conductivity of Carbon Nanotubes |journal=Phys. Rev. Lett. |volume=84 |issue=20 |pages=4613–6 |arxiv=cond-mat/0002414 |bibcode=2000PhRvL..84.4613B |doi=10.1103/PhysRevLett.84.4613 |pmid=10990753 |s2cid=9006722}}</ref> early measurements of the [[thermal conductivity]] of suspended graphene reported an exceptionally large thermal conductivity up to {{val|5300|u=W⋅m<sup>−1</sup>⋅K<sup>−1</sup>}},<ref name="Balandin">{{cite journal |last1=Balandin |first1=A. A. |last2=Ghosh |first2=Suchismita |last3=Bao |first3=Wenzhong |last4=Calizo |first4=Irene |last5=Teweldebrhan |first5=Desalegne |last6=Miao |first6=Feng |last7=Lau |first7=Chun Ning |date=20 February 2008 |title=Superior Thermal Conductivity of Single-Layer Graphene |journal=Nano Letters |volume=8 |issue=3 |pages=902–907 |bibcode=2008NanoL...8..902B |doi=10.1021/nl0731872 |pmid=18284217 |s2cid=9310741}}</ref> compared with the thermal conductivity of pyrolytic [[graphite]] of approximately {{val|2,000|u=W⋅m<sup>−1</sup>⋅K<sup>−1</sup>}} at room temperature.<ref name="Touloukian1970">{{cite book |author=Y S. Touloukian |url={{google books |plainurl=y |id=31sqAAAAYAAJ}} |title=Thermophysical Properties of Matter: Thermal conductivity: nonmetallic solids |publisher=IFI/Plenum |year=1970 |isbn=978-0-306-67020-6}}</ref> However, later studies primarily on more scalable but more defected graphene derived by Chemical Vapor Deposition have been unable to reproduce such high thermal conductivity measurements, producing a wide range of thermal conductivities between {{val|1,500}} – {{val|2,500|u=W⋅m<sup>−1</sup>⋅K<sup>−1</sup>}} for suspended single-layer graphene.<ref name="CaiMoore2010">{{cite journal |last1=Cai |first1=Weiwei |last2=Moore |first2=Arden L. |last3=Zhu |first3=Yanwu |last4=Li |first4=Xuesong |last5=Chen |first5=Shanshan |last6=Shi |first6=Li |last7=Ruoff |first7=Rodney S. |year=2010 |title=Thermal Transport in Suspended and Supported Monolayer Graphene Grown by Chemical Vapor Deposition |journal=Nano Letters |volume=10 |issue=5 |pages=1645–1651 |bibcode=2010NanoL..10.1645C |doi=10.1021/nl9041966 |pmid=20405895 |s2cid=207664146}}</ref><ref name="FaugerasFaugeras2010">{{cite journal |last1=Faugeras |first1=Clement |last2=Faugeras |first2=Blaise |last3=Orlita |first3=Milan |last4=Potemski |first4=M. |last5=Nair |first5=Rahul R. |last6=Geim |first6=A. K. |year=2010 |title=Thermal Conductivity of Graphene in Corbino Membrane Geometry |journal=ACS Nano |volume=4 |issue=4 |pages=1889–1892 |arxiv=1003.3579 |bibcode=2010arXiv1003.3579F |doi=10.1021/nn9016229 |pmid=20218666 |s2cid=207558462}}</ref><ref name="XuPereira2014">{{cite journal |last1=Xu |first1=Xiangfan |last2=Pereira |first2=Luiz F. C. |last3=Wang |first3=Yu |last4=Wu |first4=Jing |last5=Zhang |first5=Kaiwen |last6=Zhao |first6=Xiangming |last7=Bae |first7=Sukang |last8=Tinh Bui |first8=Cong |last9=Xie |first9=Rongguo |last10=Thong |first10=John T. L. |last11=Hong |first11=Byung Hee |last12=Loh |first12=Kian Ping |last13=Donadio |first13=Davide |last14=Li |first14=Baowen |last15=Özyilmaz |first15=Barbaros |year=2014 |title=Length-dependent thermal conductivity in suspended single-layer graphene |journal=Nature Communications |volume=5 |page=3689 |arxiv=1404.5379 |bibcode=2014NatCo...5.3689X |doi=10.1038/ncomms4689 |pmid=24736666 |s2cid=10617464}}</ref><ref name="LeeYoon2011">{{cite journal |last1=Lee |first1=Jae-Ung |last2=Yoon |first2=Duhee |last3=Kim |first3=Hakseong |last4=Lee |first4=Sang Wook |last5=Cheong |first5=Hyeonsik |year=2011 |title=Thermal conductivity of suspended pristine graphene measured by Raman spectroscopy |journal=Physical Review B |volume=83 |issue=8 |page=081419 |arxiv=1103.3337 |bibcode=2011PhRvB..83h1419L |doi=10.1103/PhysRevB.83.081419 |s2cid=118664500}}</ref> The large range in the reported thermal conductivity can be caused by large measurement uncertainties as well as variations in the graphene quality and processing conditions. In addition, it is known that when single-layer graphene is supported on an amorphous material, the thermal conductivity is reduced to about {{val|500}} – {{val|600|u=W⋅m<sup>−1</sup>⋅K<sup>−1</sup>}} at room temperature as a result of scattering of graphene lattice waves by the substrate,<ref name="SeolJo2010">{{cite journal |last1=Seol |first1=J. H. |last2=Jo |first2=I. |last3=Moore |first3=A. L. |last4=Lindsay |first4=L. |last5=Aitken |first5=Z. H. |last6=Pettes |first6=M. T. |last7=Li |first7=X. |last8=Yao |first8=Z. |last9=Huang |first9=R. |last10=Broido |first10=D. |last11=Mingo |first11=N. |last12=Ruoff |first12=R. S. |last13=Shi |first13=L. |year=2010 |title=Two-Dimensional Phonon Transport in Supported Graphene |url=https://hal-cea.archives-ouvertes.fr/cea-00818281 |url-status=live |journal=Science |volume=328 |issue=5975 |pages=213–216 |bibcode=2010Sci...328..213S |doi=10.1126/science.1184014 |pmid=20378814 |s2cid=213783 |archive-url=https://web.archive.org/web/20230204015608/https://hal-cea.archives-ouvertes.fr/cea-00818281 |archive-date=4 February 2023 |access-date=28 January 2023}}</ref><ref name="Klemens2001">{{cite journal |last1=Klemens |first1=P. G. |year=2001 |title=Theory of Thermal Conduction in Thin Ceramic Films |journal=International Journal of Thermophysics |volume=22 |issue=1 |pages=265–275 |doi=10.1023/A:1006776107140 |s2cid=115849714}}</ref> and can be even lower for few-layer graphene encased in amorphous oxide.<ref name="JangChen2010">{{cite journal |last1=Jang |first1=Wanyoung |last2=Chen |first2=Zhen |last3=Bao |first3=Wenzhong |last4=Lau |first4=Chun Ning |last5=Dames |first5=Chris |year=2010 |title=Thickness-Dependent Thermal Conductivity of Encased Graphene and Ultrathin Graphite |journal=Nano Letters |volume=10 |issue=10 |pages=3909–3913 |bibcode=2010NanoL..10.3909J |doi=10.1021/nl101613u |pmid=20836537 |s2cid=45253497}}</ref> Likewise, polymeric residue can contribute to a similar decrease in the thermal conductivity of suspended graphene to approximately {{val|500}} – {{val|600|u=W⋅m<sup>−1</sup>⋅K<sup>−1</sup>}} for bilayer graphene.<ref name="PettesJo2011">{{cite journal |last1=Pettes |first1=Michael Thompson |last2=Jo |first2=Insun |last3=Yao |first3=Zhen |last4=Shi |first4=Li |year=2011 |title=Influence of Polymeric Residue on the Thermal Conductivity of Suspended Bilayer Graphene |journal=Nano Letters |volume=11 |issue=3 |pages=1195–1200 |bibcode=2011NanoL..11.1195P |doi=10.1021/nl104156y |pmid=21314164}}</ref> 

Isotopic composition, specifically the ratio of [[Carbon-12|<sup>12</sup>C]] to [[Carbon-13|<sup>13</sup>C]], significantly affects graphene's thermal conductivity. Isotopically pure <sup>12</sup>C graphene exhibits higher thermal conductivity than either a 50:50 isotope ratio or the naturally occurring 99:1 ratio.<ref name="chen2012natmat">{{cite journal |last1=Chen |first1=Shanshan |last2=Wu |first2=Qingzhi |last3=Mishra |first3=Columbia |last4=Kang |first4=Junyong |last5=Zhang |first5=Hengji |last6=Cho |first6=Kyeongjae |last7=Cai |first7=Weiwei |last8=Balandin |first8=Alexander A. |last9=Ruoff |first9=Rodney S. |year=2012 |title=Thermal conductivity of isotopically modified graphene |journal=[[Nature Materials]] |publication-date=10 January 2012 |volume=11 |issue=3 |pages=203–207 |arxiv=1112.5752 |bibcode=2012NatMa..11..203C |doi=10.1038/nmat3207 |pmid=22231598 |s2cid=119228971}}<br />''Lay summary'': {{cite news |last=Tracy |first=Suzanne |date=12 January 2012 |title=Keeping Electronics Cool |url=http://www.scientificcomputing.com/news-HPC-Keeping-Electronics-Cool-011212.aspx?et_cid=2422972&et_rid=220285420&linkid=http%3a%2f%2fwww.scientificcomputing.com%2fnews-HPC-Keeping-Electronics-Cool-011212.aspx |periodical=Scientific Computing |publisher=[[Advantage Business Media]] |at=scientificcomputing.com |publication-date=12 January 2012}}</ref> It can be shown by using the [[Wiedemann–Franz law]], that the thermal conduction is [[phonon]]-dominated.<ref name="Balandin" /> However, for a gated graphene strip, an applied gate bias causing a [[Fermi energy]] shift much larger than ''k''<sub>B</sub>''T'' can cause the electronic contribution to increase and dominate over the [[phonon]] contribution at low temperatures. The ballistic thermal conductance of graphene is isotropic.<ref name="Saito2">{{cite journal |last1=Saito |first1=K. |last2=Nakamura |first2=J. |last3=Natori |first3=A. |year=2007 |title=Ballistic thermal conductance of a graphene sheet |journal=[[Physical Review B]] |volume=76 |issue=11 |page=115409 |bibcode=2007PhRvB..76k5409S |doi=10.1103/PhysRevB.76.115409}}</ref><ref name="Qizhen Liang, Xuxia Yao, Wei Wang, Yan Liu, Ching Ping Wong. 2011 2392–2401">{{cite journal |last1=Liang |first1=Qizhen |last2=Yao |first2=Xuxia |last3=Wang |first3=Wei |last4=Liu |first4=Yan |last5=Wong |first5=Ching Ping |year=2011 |title=A Three-Dimensional Vertically Aligned Functionalized Multilayer Graphene Architecture: An Approach for Graphene-Based Thermal Interfacial Materials |url=https://figshare.com/articles/A_Three_Dimensional_Vertically_Aligned_Functionalized_Multilayer_Graphene_Architecture_An_Approach_for_Graphene_Based_Thermal_Interfacial_Materials/2680561 |url-status=live |journal=ACS Nano |volume=5 |issue=3 |pages=2392–2401 |doi=10.1021/nn200181e |pmid=21384860 |archive-url=https://web.archive.org/web/20200801041807/https://figshare.com/articles/A_Three_Dimensional_Vertically_Aligned_Functionalized_Multilayer_Graphene_Architecture_An_Approach_for_Graphene_Based_Thermal_Interfacial_Materials/2680561 |archive-date=1 August 2020 |access-date=1 December 2019}}</ref>

Graphite, a 3D counterpart to graphene, exhibits a [[basal plane]] [[thermal conductivity]] exceeding {{val|1,000|u=W⋅m<sup>−1</sup>⋅K<sup>−1</sup>}} (similar to [[diamond]]), In graphite, the c-axis (out of plane) thermal conductivity is over a factor of ~100 smaller due to the weak binding forces between basal planes as well as the larger [[lattice spacing]].<ref>{{cite book |last=Delhaes |first=P. |url={{google books |plainurl=y |id=7p2pgNOWPbEC}} |title=Graphite and Precursors |publisher=CRC Press |year=2001 |isbn=978-90-5699-228-6}}</ref> In addition, the ballistic thermal conductance of graphene is shown to give the lower limit of the ballistic thermal conductance, per unit circumference, length of carbon nanotubes.<ref name="mingo">{{cite journal |last1=Mingo |first1=N. |last2=Broido |first2=D.A. |year=2005 |title=Carbon Nanotube Ballistic Thermal Conductance and Its Limits |journal=Physical Review Letters |volume=95 |issue=9 |page=096105 |bibcode=2005PhRvL..95i6105M |doi=10.1103/PhysRevLett.95.096105 |pmid=16197233}}</ref>

Graphene's thermal conductivity is influenced by its three [[acoustic phonon]] modes: two linear [[dispersion relation]] dispersion relation in-plane modes (LA, TA) and one quadratic dispersion relation out-of-plane mode (ZA). At low temperatures, the dominance of the T<sup>1.5</sup> thermal conductivity contribution of the out-of-plane mode supersedes the ''T''<sup>2</sup> dependence of the linear modes.<ref name="mingo" /> Some graphene phonon bands exhibit negative [[Grüneisen parameter]]s,<ref name="mounet">{{cite journal |last1=Mounet |first1=N. |last2=Marzari |first2=N. |year=2005 |title=First-principles determination of the structural, vibrational and thermodynamic properties of diamond, graphite, and derivatives |journal=Physical Review B |volume=71 |issue=20 |page=205214 |arxiv=cond-mat/0412643 |bibcode=2005PhRvB..71t5214M |doi=10.1103/PhysRevB.71.205214 |s2cid=119461729}}</ref> resulting in negative [[thermal expansion coefficient]] at low temperatures. The lowest negative Grüneisen parameters correspond to the lowest transverse acoustic ZA modes, whose frequencies increase with in-plane [[lattice parameter]], akin to a stretched string with higher frequency vibrations.<ref name="lifshitz">{{cite book |last=Lifshitz |first=I.M. |title=Journal of Experimental and Theoretical Physics |year=1952 |volume=22 |page=475 |language=ru}}</ref>

=== Chemical properties ===

Graphene has a theoretical [[specific surface area]] (SSA) of {{val|2630 |ul=m2 |up=g}}. This is much larger than that reported to date for carbon black (typically smaller than {{val|900 |ul=m2 |up=g}}) or for carbon nanotubes (CNTs), from ≈100 to {{val|1000 |ul=m2 |up=g}} and is similar to [[activated carbon]].<ref name="bonaccorso2015">{{cite journal |doi=10.1126/science.1246501 |pmid=25554791 |title=Graphene, related two-dimensional crystals, and hybrid systems for energy conversion and storage |journal=Science |volume=347 |issue=6217 |page=1246501 |year=2015 |last1=Bonaccorso |first1=F. |last2=Colombo |first2=L. |last3=Yu |first3=G. |last4=Stoller |first4=M. |last5=Tozzini |first5=V. |last6=Ferrari |first6=A. C. |last7=Ruoff |first7=R. S. |last8=Pellegrini |first8=V. |bibcode=2015Sci...347...41B|s2cid=6655234 }}</ref>
Graphene is the only form of carbon (or solid material) in which every atom is available for chemical reaction from two sides (due to the 2D structure). Atoms at the edges of a graphene sheet have special chemical reactivity. Graphene has the highest ratio of edge atoms of any [[allotrope]]. Defects within a sheet increase its chemical reactivity.<ref name="denis2013"/> The onset temperature of reaction between the basal plane of single-layer graphene and oxygen gas is below {{convert|260|C|K|sigfig=2}}.<ref name="Yamada3"/> Graphene burns at very low temperatures (e.g., {{convert|350|C|K|sigfig=2}}).<ref name="Eftekhari"/> Graphene is commonly modified with oxygen- and nitrogen-containing [[Functional group|functional groups]] and analyzed by [[infrared spectroscopy]] and [[X-ray photoelectron spectroscopy]]. However, the determination of structures of graphene with oxygen-<ref name="Yamada1"/> and nitrogen-<ref name="Yamada2"/> functional groups require the structures to be well controlled.

In 2013, [[Stanford University]] physicists reported that single-layer graphene is a hundred times more chemically reactive than thicker multilayer sheets.<ref>{{cite news |url=http://phys.org/news/2013-02-thinnest-graphene-sheets-react-strongly.html |title=Thinnest graphene sheets react strongly with hydrogen atoms; thicker sheets are relatively unaffected |work=Phys.org |date=1 February 2013 |access-date=14 December 2013 |archive-date=24 September 2018 |archive-url=https://web.archive.org/web/20180924213239/https://phys.org/news/2013-02-thinnest-graphene-sheets-react-strongly.html |url-status=live }}</ref>

Graphene can self-repair holes in its sheets, when exposed to molecules containing carbon, such as [[hydrocarbon]]s. Bombarded with pure carbon atoms, the atoms perfectly align into [[hexagon]]s, filling the holes.<ref name=zan2012/><ref name=puiu2012/>

=== Biological properties ===

Despite the promising results in different cell studies and proof of concept studies, there is still incomplete understanding of the full biocompatibility of graphene-based materials.<ref>{{cite journal |last1=Bullock |first1=Christopher J. |last2=Bussy |first2=Cyrill |title=Biocompatibility Considerations in the Design of Graphene Biomedical Materials |journal=Advanced Materials Interfaces |date=18 April 2019 |volume=6 |issue=11 |page=1900229 |doi=10.1002/admi.201900229 |doi-access=free }}</ref> Different cell lines react differently when exposed to graphene, and it has been shown that the lateral size of the graphene flakes, the form and surface chemistry can elicit different biological responses on the same cell line.<ref>{{cite journal |last1=Liao |first1=Ken-Hsuan |last2=Lin |first2=Yu-Shen |last3=Macosko |first3=Christopher W. |last4=Haynes |first4=Christy L. |title=Cytotoxicity of Graphene Oxide and Graphene in Human Erythrocytes and Skin Fibroblasts |journal=ACS Applied Materials & Interfaces |date=27 July 2011 |volume=3 |issue=7 |pages=2607–2615 |doi=10.1021/am200428v |pmid=21650218 }}</ref>

There are indications that graphene has promise as a useful material for interacting with neural cells; studies on cultured neural cells show limited success.<ref>{{cite journal |last1=Fabbro |first1=Alessandra |last2=Scaini |first2=Denis |last3=León |first3=Verónica |last4=Vázquez |first4=Ester |last5=Cellot |first5=Giada |last6=Privitera |first6=Giulia |last7=Lombardi |first7=Lucia |last8=Torrisi |first8=Felice |last9=Tomarchio |first9=Flavia |last10=Bonaccorso |first10=Francesco |last11=Bosi |first11=Susanna |last12=Ferrari |first12=Andrea C. |last13=Ballerini |first13=Laura |last14=Prato |first14=Maurizio |title=Graphene-Based Interfaces Do Not Alter Target Nerve Cells |journal=ACS Nano |date=26 January 2016 |volume=10 |issue=1 |pages=615–623 |doi=10.1021/acsnano.5b05647 |pmid=26700626 |hdl=11368/2860012 |hdl-access=free }}</ref><ref>{{cite web |title=Graphene shown to safely interact with neurons in the brain |url=https://www.cam.ac.uk/research/news/graphene-shown-to-safely-interact-with-neurons-in-the-brain |website=University of Cambridge |date=2016-01-29 |access-date=2016-02-16 |archive-date=23 February 2016 |archive-url=https://web.archive.org/web/20160223124743/https://www.cam.ac.uk/research/news/graphene-shown-to-safely-interact-with-neurons-in-the-brain |url-status=live }}</ref>

Graphene also has some utility in [[osteogenic|osteogenesi]]s. Researchers at the Graphene Research Centre at the [[National University of Singapore]] (NUS) discovered in 2011 the ability of graphene to accelerate the osteogenic differentiation of human [[Mesenchymal stem cell|mesenchymal stem cells]] without the use of biochemical inducers.<ref>{{cite journal |last1=Nayak |first1=Tapas R. |last2=Andersen |first2=Henrik |last3=Makam |first3=Venkata S. |last4=Khaw |first4=Clement |last5=Bae |first5=Sukang |last6=Xu |first6=Xiangfan |last7=Ee |first7=Pui-Lai R. |last8=Ahn |first8=Jong-Hyun |last9=Hong |first9=Byung Hee |last10=Pastorin |first10=Giorgia |last11=Özyilmaz |first11=Barbaros |title=Graphene for Controlled and Accelerated Osteogenic Differentiation of Human Mesenchymal Stem Cells |journal=ACS Nano |date=28 June 2011 |volume=5 |issue=6 |pages=4670–4678 |doi=10.1021/nn200500h |pmid=21528849 |bibcode=2011arXiv1104.5120N |arxiv=1104.5120 |s2cid=20794090 }}</ref>

Graphene can be used in biosensors; in 2015, researchers demonstrated that a graphene-based sensor can be used to detect a cancer risk biomarker. In particular, by using epitaxial graphene on silicon carbide, they were repeatedly able to detect 8-hydroxydeoxyguanosine (8-OHdG), a DNA damage biomarker.<ref>{{Cite journal |title=Generic epitaxial graphene biosensors for ultrasensitive detection of cancer risk biomarker |last=Tehrani |first=Z. |date=2014-09-01 |journal=2D Materials |doi=10.1088/2053-1583/1/2/025004 |bibcode=2014TDM.....1b5004T |volume=1 |issue=2 |page=025004 |s2cid=55035225 |url=https://cronfa.swan.ac.uk/Record/cronfa19735/Download/0019735-07052015130054.pdf |access-date=7 January 2020 |archive-date=1 August 2020 |archive-url=https://web.archive.org/web/20200801050028/https://cronfa.swan.ac.uk/Record/cronfa19735/Download/0019735-07052015130054.pdf |url-status=live }}</ref>

=== Support substrate ===

The electronic property of graphene can be significantly influenced by the supporting substrate. Studies of graphene monolayers on clean and hydrogen(H)-passivated silicon (100) (Si(100)/H) surfaces have been performed.<ref>{{cite journal|last1=Xu|first1=Yang|last2=He|first2=K. T.|last3=Schmucker|first3=S. W.|last4=Guo|first4=Z.|last5=Koepke|first5=J. C.|last6=Wood|first6=J. D.|last7=Lyding|first7=J. W.|last8=Aluru|first8=N. R.|s2cid=207573621|title=Inducing Electronic Changes in Graphene through Silicon (100) Substrate Modification|journal=Nano Letters|volume=11|issue=7|pages=2735–2742|date=2011|doi=10.1021/nl201022t|pmid=21661740|bibcode=2011NanoL..11.2735X}}</ref> The Si(100)/H surface does not perturb the electronic properties of graphene, whereas the interaction between the clean Si(100) surface and graphene changes the electronic states of graphene significantly. This effect results from the covalent bonding between C and surface Si atoms, modifying the π-orbital network of the graphene layer. The local density of states shows that the bonded C and Si surface states are highly disturbed near the Fermi energy.

== Graphene layers and structural variants ==
=== Monolayer sheets ===

In 2013 a group of Polish scientists presented a production unit that allows the manufacture of continuous monolayer sheets.<ref>{{cite journal |title=Single and Multilayer Growth of Graphene from the Liquid Phase |journal=Applied Mechanics and Materials |volume=510 |pages=8–12 |doi=10.4028/www.scientific.net/AMM.510.8 |year=2014 |last1=Kula |first1=Piotr |last2=Pietrasik |first2=Robert |last3=Dybowski |first3=Konrad |last4=Atraszkiewicz |first4=Radomir |last5=Szymanski |first5=Witold |last6=Kolodziejczyk |first6=Lukasz |last7=Niedzielski |first7=Piotr |last8=Nowak |first8=Dorota |s2cid=93345920 }}</ref> The process is based on graphene growth on a liquid metal matrix.<ref>{{cite web |title=Polish scientists find way to make super-strong graphene sheets {{!}} Graphene-Info |url=http://www.graphene-info.com/polish-scientists-find-way-make-super-strong-graphene-sheets |website=www.graphene-info.com |access-date=2015-07-01 |archive-date=1 July 2015 |archive-url=https://web.archive.org/web/20150701184231/http://www.graphene-info.com/polish-scientists-find-way-make-super-strong-graphene-sheets |url-status=live }}</ref> The product of this process was called [[HSMG|High Strength Metallurgical Graphene]]. In a new study published in Nature, the researchers have used a single-layer graphene electrode and a novel surface-sensitive non-linear spectroscopy technique to investigate the top-most water layer at the electrochemically charged surface. They found that the interfacial water response to the applied electric field is asymmetric concerning the nature of the applied field.<ref>{{cite journal |last1=Montenegro |first1=Angelo |last2=Dutta |first2=Chayan |last3=Mammetkuliev |first3=Muhammet |last4=Shi |first4=Haotian |last5=Hou |first5=Bingya |last6=Bhattacharyya |first6=Dhritiman |last7=Zhao |first7=Bofan |last8=Cronin |first8=Stephen B. |last9=Benderskii |first9=Alexander V. |title=Asymmetric response of interfacial water to applied electric fields |journal=Nature |date=3 June 2021 |volume=594 |issue=7861 |pages=62–65 |doi=10.1038/s41586-021-03504-4 |pmid=34079138 |bibcode=2021Natur.594...62M |s2cid=235321882 }}</ref>

=== Bilayer graphene ===
{{main|Bilayer graphene}}

Bilayer graphene displays the [[anomalous quantum Hall effect]], a tunable [[band gap]]<ref name="PRB75.155115">{{cite journal |doi=10.1103/PhysRevB.75.155115 |title=Ab initio theory of gate induced gaps in graphene bilayers |year=2007 |last1=Min |first1=Hongki |last2=Sahu |first2=Bhagawan |last3=Banerjee |first3=Sanjay |last4=MacDonald |first4=A. |journal=Physical Review B |volume=75 |issue=15 |page=155115 |arxiv=cond-mat/0612236 |bibcode=2007PhRvB..75o5115M|s2cid=119443126 }}</ref> and potential for [[Exciton#Interaction|excitonic condensation]]<ref name="PRL104.096802">{{cite journal |doi=10.1103/PhysRevLett.104.096802 |pmid=20367001 |title=Anomalous Exciton Condensation in Graphene Bilayers |year=2010 |last1=Barlas |first1=Yafis |last2=Côté |first2=R. |last3=Lambert |first3=J. |last4=MacDonald |first4=A. H. |journal=Physical Review Letters |volume=104 |issue=9 |page=96802 |bibcode=2010PhRvL.104i6802B |arxiv=0909.1502|s2cid=33249360 }}</ref>&nbsp;–making it a promising candidate for [[optoelectronic]] and [[nanoelectronic]] applications. Bilayer graphene typically can be found either in [[Twistronics|twisted]] configurations where the two layers are rotated relative to each other or graphitic Bernal stacked configurations where half the atoms in one layer lie atop half the atoms in the other.<ref name="nl204547v">{{cite journal |doi=10.1021/nl204547v |pmid=22329410 |title=Twinning and Twisting of Tri- and Bilayer Graphene |year=2012 |last1=Min |first1=Lola |last2=Hovden |first2=Robert |last3=Huang |journal=Nano Letters |volume=12 |issue=3 |first3=Pinshane |last4=Wojcik |first4=Michal |last5=Muller |first5=David A. |last6=Park |first6=Jiwoong |s2cid=896422 |pages=1609–1615 |bibcode=2012NanoL..12.1609B}}</ref> Stacking order and orientation govern the optical and electronic properties of bilayer graphene.

One way to synthesize bilayer graphene is via [[chemical vapor deposition]], which can produce large bilayer regions that almost exclusively conform to a Bernal stack geometry.<ref name="nl204547v" />

It has been shown that the two graphene layers can withstand important strain or doping mismatch<ref>{{cite journal |last1=Forestier |first1=Alexis |last2=Balima |first2=Félix |last3=Bousige |first3=Colin |last4=de Sousa Pinheiro |first4=Gardênia |last5=Fulcrand |first5=Rémy |last6=Kalbác |first6=Martin |last7=San-Miguel |first7=Alfonso |title=Strain and Piezo-Doping Mismatch between Graphene Layers |journal=J. Phys. Chem. C |date=April 28, 2020 |volume=124 |issue=20 |page=11193 |doi=10.1021/acs.jpcc.0c01898 |s2cid=219011027 |url=https://hal.archives-ouvertes.fr/hal-02651267/document |access-date=21 December 2020 |archive-date=29 April 2021 |archive-url=https://web.archive.org/web/20210429043452/https://hal.archives-ouvertes.fr/hal-02651267/document |url-status=live }}</ref> which ultimately should lead to their exfoliation.

=== Turbostratic ===

Turbostratic graphene exhibits weak interlayer coupling, and the spacing is increased with respect to Bernal-stacked multilayer graphene. Rotational misalignment preserves the 2D electronic structure, as confirmed by [[Raman spectroscopy]].<ref name="turbostratic-raman">{{cite journal|last1=Lenski |first1=Daniel R. |last2=Fuhrer |first2=Michael S. |title=Raman and optical characterization of multilayer turbostratic graphene grown via chemical vapor deposition |year=2011|doi=10.1063/1.3605545|journal=Journal of Applied Physics|volume=110|issue=1 |pages=013720–013720–4 |arxiv=1011.1683|bibcode=2011JAP...110a3720L }}</ref> The D peak is very weak, whereas the 2D and G peaks remain prominent.<ref name="turbostratic-raman"/>

A rather peculiar feature is that the I<sub>2D</sub>/I<sub>G</sub> ratio can exceed 10. However, most importantly, the M peak, which originates from AB stacking, is absent, whereas the TS<sub>1</sub> and TS<sub>2</sub> modes are visible in the [[Raman spectrum]].<ref name="Luong 647–651">{{Cite journal|last1=Luong|first1=Duy X.|last2=Bets|first2=Ksenia V.|last3=Algozeeb|first3=Wala Ali|last4=Stanford|first4=Michael G.|last5=Kittrell|first5=Carter|last6=Chen|first6=Weiyin|last7=Salvatierra|first7=Rodrigo V.|last8=Ren|first8=Muqing|last9=McHugh|first9=Emily A.|last10=Advincula|first10=Paul A.|last11=Wang|first11=Zhe|date=January 2020|title=Gram-scale bottom-up flash graphene synthesis|url=https://www.nature.com/articles/s41586-020-1938-0|journal=Nature|language=en|volume=577|issue=7792|pages=647–651|doi=10.1038/s41586-020-1938-0|pmid=31988511|bibcode=2020Natur.577..647L|s2cid=210926149|issn=1476-4687|access-date=16 October 2021|archive-date=20 October 2021|archive-url=https://web.archive.org/web/20211020123054/https://www.nature.com/articles/s41586-020-1938-0|url-status=live}}</ref><ref>{{Cite journal|last1=Stanford|first1=Michael G.|last2=Bets|first2=Ksenia V.|last3=Luong|first3=Duy X.|last4=Advincula|first4=Paul A.|last5=Chen|first5=Weiyin|last6=Li|first6=John Tianci|last7=Wang|first7=Zhe|last8=McHugh|first8=Emily A.|last9=Algozeeb|first9=Wala A.|last10=Yakobson|first10=Boris I.|last11=Tour|first11=James M.|date=2020-10-27|title=Flash Graphene Morphologies|url=https://doi.org/10.1021/acsnano.0c05900|journal=ACS Nano|volume=14|issue=10|pages=13691–13699|doi=10.1021/acsnano.0c05900|pmid=32909736|osti=1798502 |s2cid=221623214|issn=1936-0851}}</ref> The material is formed through conversion of non-graphenic carbon into graphenic carbon without providing sufficient energy to allow for the reorganization through annealing of adjacent graphene layers into crystalline graphitic structures.

=== Graphene superlattices ===

Periodically stacked graphene and its insulating isomorph provide a fascinating structural element in implementing highly functional superlattices at the atomic scale, which offers possibilities for designing nanoelectronic and photonic devices. Various types of superlattices can be obtained by stacking graphene and its related forms.<ref>{{cite journal|last1=Xu|first1=Yang|last2=Liu|first2=Yunlong|last3=Chen|first3=Huabin|last4=Lin|first4=Xiao|last5=Lin|first5=Shisheng|last6=Yu|first6=Bin|last7=Luo|first7=Jikui|title=Ab initio study of energy-band modulation in graphene-based two-dimensional layered superlattices|journal=Journal of Materials Chemistry|volume=22|issue=45|pages=23821|date=2012|doi=10.1039/C2JM35652J}}</ref> The energy band in layer-stacked superlattices is found to be more sensitive to the barrier width than that in conventional III–V semiconductor superlattices. When adding more than one atomic layer to the barrier in each period, the coupling of electronic wavefunctions in neighboring potential wells can be significantly reduced, which leads to the degeneration of continuous subbands into quantized energy levels. When varying the well width, the energy levels in the potential wells along the L-M direction behave distinctly from those along the K-H direction.

A superlattice corresponds to a periodic or quasi-periodic arrangement of different materials and can be described by a superlattice period which confers a new translational symmetry to the system, impacting their phonon dispersions and subsequently their thermal transport properties. Recently, uniform monolayer graphene-hBN structures have been successfully synthesized via lithography patterning coupled with chemical vapor deposition (CVD).<ref>{{cite journal |last1=Liu |first1=Zheng |last2=Ma |first2=Lulu |last3=Shi |first3=Gang |last4=Zhou |first4=Wu |last5=Gong |first5=Yongji |last6=Lei |first6=Sidong |last7=Yang |first7=Xuebei |last8=Zhang |first8=Jiangnan |last9=Yu |first9=Jingjiang |last10=Hackenberg |first10=Ken P. |last11=Babakhani |first11=Aydin |last12=Idrobo |first12=Juan-Carlos |last13=Vajtai |first13=Robert |last14=Lou |first14=Jun |last15=Ajayan |first15=Pulickel M. |title=In-plane heterostructures of graphene and hexagonal boron nitride with controlled domain sizes |url=https://www.nature.com/articles/nnano.2012.256 |journal=Nature Nanotechnology |pages=119–124 |language=en |doi=10.1038/nnano.2012.256 |date=February 2013 |volume=8 |issue=2 |pmid=23353677 |bibcode=2013NatNa...8..119L |access-date=1 December 2020 |archive-date=7 April 2023 |archive-url=https://web.archive.org/web/20230407181357/https://www.nature.com/articles/nnano.2012.256 |url-status=live }}</ref> Furthermore, superlattices of graphene-HBN are ideal model systems for the realization and understanding of coherent (wave-like) and incoherent (particle-like) phonon thermal transport.<ref>{{cite journal |last1=Felix |first1=Isaac M. |last2=Pereira |first2=Luiz Felipe C. |title=Thermal Conductivity of Graphene-hBN Superlattice Ribbons |url= |journal=Scientific Reports |pages=2737 |language=en |doi=10.1038/s41598-018-20997-8 |date=9 February 2018|volume=8 |issue=1 |pmid=29426893 |pmc=5807325 |bibcode=2018NatSR...8.2737F }}</ref><ref>{{cite journal |last1=Felix |first1=Isaac M. |last2=Pereira |first2=Luiz Felipe C. |title=Suppression of coherent thermal transport in quasiperiodic graphene-hBN superlattice ribbons |url=https://doi.org/10.1016/j.carbon.2019.12.090 |journal=Carbon |pages=335–341 |doi=10.1016/j.carbon.2019.12.090 |date=April 2020|volume=160 |arxiv=2001.03072 |bibcode=2020Carbo.160..335F |s2cid=210116531 }}</ref><ref>{{cite journal |last1=Felix |first1=Isaac M. |last2=Pereira |first2=Luiz Felipe C. |title=Thermal conductivity of Thue–Morse and double-period quasiperiodic graphene-hBN superlattices |url=https://www.sciencedirect.com/science/article/abs/pii/S0017931021015623 |journal=International Journal of Heat and Mass Transfer |pages=122464 |language=en |doi=10.1016/j.ijheatmasstransfer.2021.122464 |date=1 May 2022 |volume=186 |bibcode=2022IJHMT.18622464F |s2cid=245712349 |access-date=6 January 2022 |archive-date=6 January 2022 |archive-url=https://web.archive.org/web/20220106140014/https://www.sciencedirect.com/science/article/abs/pii/S0017931021015623 |url-status=live }}</ref><ref>{{cite thesis |last1=Félix |first1=Isaac de Macêdo |title=Transporte térmico em nanofitas de grafeno-nitreto de boro |date=29 March 2016 |publisher=Brasil |url=https://repositorio.ufrn.br/jspui/handle/123456789/21498 |type=masterThesis |access-date=6 January 2022 |archive-date=5 March 2022 |archive-url=https://web.archive.org/web/20220305094427/https://repositorio.ufrn.br/jspui/handle/123456789/21498 |url-status=live }}</ref><ref>{{cite thesis |last1=Félix |first1=Isaac de Macêdo |title=Condução de calor em nanofitas quase-periódicas de grafeno-hBN |url=https://repositorio.ufrn.br/handle/123456789/30749 |language=pt-BR |date=4 August 2020 |publisher=Universidade Federal do Rio Grande do Norte |type=doctoralThesis |access-date=1 December 2020 |archive-date=2 February 2021 |archive-url=https://web.archive.org/web/20210202054317/https://repositorio.ufrn.br/handle/123456789/30749 |url-status=live }} [[File:CC-BY icon.svg|50px]]  Text was copied from this source, which is available under a [https://creativecommons.org/licenses/by/4.0/  Creative Commons Attribution 4.0 International License] {{Webarchive|url=https://web.archive.org/web/20171016050101/https://creativecommons.org/licenses/by/4.0/ |date=16 October 2017 }}.</ref>

== Nanostructured graphene forms ==
=== Graphene nanoribbons ===
[[File:Graphene edge names.svg|thumb|upright=1.2|Names for graphene edge topologies]]
[[File:Cnt zz v3.gif|thumb|upright=1.5|[[Graphene nanoribbon|GNR]] Electronic band structure of graphene strips of varying widths in zig-zag orientation. Tight-binding calculations show that they are all metallic.]]
[[File:Cnt gnrarm v3.gif|thumb|upright=1.5|[[Graphene nanoribbon|GNR]] Electronic band structure of graphene strips of various widths in the armchair orientation. Tight-binding calculations show that they are semiconducting or metallic depending on width (chirality).]]

[[Graphene nanoribbons]] ("nanostripes" in the "zig-zag"/"zigzag" orientation), at low temperatures, show spin-polarized metallic edge currents, which also suggests applications in the new field of [[spintronics]]. (In the "armchair" orientation, the edges behave like semiconductors.<ref name="Castro">{{cite journal |first1=A Castro |last1=Neto |last2=Peres |first2=N. M. R. |last3=Novoselov |first3=K. S. |last4=Geim |first4=A. K. |last5=Geim |first5=A. K. |title=The electronic properties of graphene |journal=Rev Mod Phys |volume=81 |issue=1 |year=2009 |pages=109–162 |url=http://onnes.ph.man.ac.uk/nano/Publications/RMP_2009.pdf |archive-url=https://web.archive.org/web/20101115121052/http://onnes.ph.man.ac.uk/nano/Publications/RMP_2009.pdf |url-status=dead |archive-date=2010-11-15 |bibcode=2009RvMP...81..109C |doi=10.1103/RevModPhys.81.109 |arxiv=0709.1163|hdl=10261/18097 |s2cid=5650871 }}</ref>) 

=== Graphene quantum dots ===

A [[graphene quantum dot]] (GQD) is a graphene fragment with a size lesser than 100&nbsp;nm. The properties of GQDs are different from bulk graphene due to the quantum confinement effects which only become apparent when the size is smaller than 100&nbsp;nm.<ref name=tang2014/><ref name=tang2012/><ref name=tang2013/>

== Modified and functionalized graphene ==
{{Main|Graphene chemistry}}

=== Graphene oxide ===
{{further|Graphite oxide}}

Graphene oxide is usually produced through chemical exfoliation of graphite. A particularly popular technique is the improved [[Hummers' method]].<ref>{{Cite journal|last1=Marcano|first1=Daniela C.|last2=Kosynkin|first2=Dmitry V.|last3=Berlin|first3=Jacob M.|last4=Sinitskii|first4=Alexander|last5=Sun|first5=Zhengzong|last6=Slesarev|first6=Alexander|last7=Alemany|first7=Lawrence B.|last8=Lu|first8=Wei|last9=Tour|first9=James M.|date=2010-08-24|title=Improved Synthesis of Graphene Oxide|url=https://doi.org/10.1021/nn1006368|journal=ACS Nano|volume=4|issue=8|pages=4806–4814|doi=10.1021/nn1006368|pmid=20731455|issn=1936-0851}}</ref> Using paper-making techniques on dispersed, oxidized and chemically processed graphite in water, the monolayer flakes form a single sheet and create strong bonds. These sheets, called [[graphene oxide paper]], have a measured [[tensile modulus]] of 32 [[GPa]].<ref>{{cite web |url=http://invo.northwestern.edu/technologies/detail/graphene-oxide-paper |archive-url=https://web.archive.org/web/20160602213039/http://invo.northwestern.edu/technologies/detail/graphene-oxide-paper |archive-date=2 June 2016 |title=Graphene Oxide Paper |publisher=Northwestern University |access-date=28 February 2011}}</ref> The chemical property of graphite oxide is related to the functional groups attached to graphene sheets. These can change the [[polymerization]] pathway and similar chemical processes.<ref>{{cite journal |last1=Eftekhari |first1=Ali |last2=Yazdani |first2=Bahareh |title=Initiating electropolymerization on graphene sheets in graphite oxide structure |journal=Journal of Polymer Science Part A: Polymer Chemistry |volume=48 |pages=2204–2213 |year=2010 |doi=10.1002/pola.23990 |bibcode=2010JPoSA..48.2204E |issue=10}}</ref> Graphene oxide flakes in [[polymers]]s display enhanced photo-conducting properties.<ref>{{cite journal |last1=Nalla |first1=Venkatram |last2=Polavarapu |first2=L |last3=Manga |first3=KK |last4=Goh |first4=BM |last5=Loh |first5=KP |last6=Xu |first6=QH |last7=Ji |first7=W |title=Transient photoconductivity and femtosecond nonlinear optical properties of a conjugated polymer–graphene oxide composite |journal=Nanotechnology |volume=21 |issue=41 |page=415203 |year=2010 |pmid=20852355 |doi=10.1088/0957-4484/21/41/415203 |bibcode=2010Nanot..21O5203N|s2cid=24385952 }}</ref> Graphene is normally [[Hydrophobe|hydrophobic]] and impermeable to all gases and liquids (vacuum-tight). However, when formed into a graphene oxide-based capillary membrane, both liquid water and water vapor flow through as quickly as if the membrane were not present.<ref name="pmid22282806">{{cite journal |title=Unimpeded permeation of water through helium-leak-tight graphene-based membranes |doi=10.1126/science.1211694 |year=2012 |journal=Science |volume=335 |issue=6067 |pages=442–4 |pmid=22282806 |arxiv=1112.3488 |last1=Nair |first1=R. R. |last2=Wu |first2=H. A. |last3=Jayaram |first3=P. N. |last4=Grigorieva |first4=I. V. |last5=Geim |first5=A. K. |bibcode=2012Sci...335..442N|s2cid=15204080 }}</ref>

In 2022, researchers evaluated the biological effects of low doses on graphene oxide on larvae and imago of ''[[Drosophila melanogaster]]''. Results show that oral administration of graphene oxide at concentrations of 0.02-1% has a beneficial effect on the developmental rate and hatching ability of larvae. Long-term administration of a low dose of graphene oxide extends the lifespan of Drosophila and significantly enhances resistance to environmental stresses. These suggest that graphene oxide affects carbohydrate and lipid metabolism in adult Drosophila. These findings might provide a useful reference to assess the biological effects of graphene oxide, which could play an important role in a variety of graphene-based biomedical applications.<ref name="Evaluation of biological effects of graphene oxide using Drosophila">{{cite journal |last1=Strilbytska |first1=Olha |last2=Semaniuk |first2=Uliana |last3=Burdyliuk |first3=Nadia |last4=Lushchak |first4=Oleh |title=Evaluation of biological effects of graphene oxide using Drosophila |url=https://journals.pnu.edu.ua/index.php/pcss/article/view/5751 |journal=Physics and Chemistry of Solid State |year=2022 |volume=2 |issue=23 |pages=242–248 |doi=10.15330/pcss.23.2.242-248 |s2cid=248823106 |doi-access=free |access-date=6 February 2023 |archive-date=6 February 2023 |archive-url=https://web.archive.org/web/20230206095248/https://journals.pnu.edu.ua/index.php/pcss/article/view/5751 |url-status=live }}</ref>

=== Chemical modification ===

[[File:slgo.jpg|left|upright=1.3|thumb|Photograph of single-layer graphene oxide undergoing high temperature chemical treatment, resulting in sheet folding and loss of carboxylic functionality, or through room temperature carbodiimide treatment, collapsing into star-like clusters.]] Soluble fragments of graphene can be prepared in the laboratory through chemical modification of graphite.<ref>{{cite journal |last1=Niyogi |first1=Sandip |last2=Bekyarova |first2=Elena |last3=Itkis |first3=Mikhail E. |last4=McWilliams |first4=Jared L. |last5=Hamon |first5=Mark A. |last6=Haddon |first6=Robert C. |year=2006 |title=Solution Properties of Graphite and Graphene |journal=[[J. Am. Chem. Soc.]] |volume=128 |issue=24 |pages=7720–7721 |doi=10.1021/ja060680r |pmid=16771469|bibcode=2006JAChS.128.7720N }}</ref> First, microcrystalline graphite is treated with an acidic mixture of sulfuric acid and [[nitric acid]]. A series of oxidation and exfoliation steps produce small graphene plates with [[carboxyl]] groups at their edges. These are converted to [[acid chloride]] groups by treatment with [[thionyl chloride]]; next, they are converted to the corresponding graphene [[amide]] via treatment with octadecyl amine. The resulting material (circular graphene layers of {{convert|5.3|angstrom|m|abbr=on|lk=on|disp=or}} thickness) is soluble in [[tetrahydrofuran]], [[tetrachloromethane]] and [[1,2-Dichloroethane|dichloroethane]].

Refluxing single-layer graphene oxide (SLGO) in [[solvent]]s leads to size reduction and folding of individual sheets as well as loss of carboxylic group functionality, by up to 20%, indicating thermal instabilities of SLGO sheets dependent on their preparation methodology. When using thionyl chloride, [[acyl chloride]] groups result, which can then form aliphatic and aromatic amides with a reactivity conversion of around 70–80%.

[[File:Graphene chemistry.jpg|upright=2|thumb|Boehm titration results for various chemical reactions of single-layer graphene oxide, which reveal reactivity of the carboxylic groups and the resultant stability of the SLGO sheets after treatment.]]

[[Hydrazine]] reflux is commonly used for reducing SLGO to SLG(R), but [[titration]]s show that only around 20–30% of the carboxylic groups are lost, leaving a significant number available for chemical attachment. Analysis of SLG(R) generated by this route reveals that the system is unstable and using a room temperature stirring with [[hydrochloric acid]] (< 1.0 M) leads to around 60% loss of COOH functionality. Room temperature treatment of SLGO with [[carbodiimide]]s leads to the collapse of the individual sheets into star-like clusters that exhibited poor subsequent reactivity with amines (c. 3–5% conversion of the intermediate to the final amide).<ref>{{cite journal |first1=Raymond L.D. |last1=Whitby |first2=Alina |last2=Korobeinyk |first3=Katya V. |last3=Glevatska |title=Morphological changes and covalent reactivity assessment of single-layer graphene oxides under carboxylic group-targeted chemistry |journal=[[Carbon (journal)|Carbon]] |volume=49 |issue=2 |pages=722–725 |year=2011 |doi=10.1016/j.carbon.2010.09.049|bibcode=2011Carbo..49..722W }}</ref> It is apparent that conventional chemical treatment of carboxylic groups on SLGO generates morphological changes of individual sheets that leads to a reduction in chemical reactivity, which may potentially limit their use in composite synthesis. Therefore, chemical reaction types have been explored. SLGO has also been grafted with [[Polyallylamine hydrochloride|polyallylamine]], cross-linked through [[epoxy]] groups. When filtered into graphene oxide paper, these composites exhibit increased stiffness and strength relative to unmodified graphene oxide paper.<ref>{{cite journal |first1=Sungjin |last1=Park |first2=Dmitriy A. |last2=Dikin |first3=SonBinh T. |last3=Nguyen |first4=Rodney S. |last4=Ruoff |s2cid=55033112 |title=Graphene Oxide Sheets Chemically Cross-Linked by Polyallylamine |journal=[[J. Phys. Chem. C]] |volume=113 |pages=15801–15804 |year=2009 |doi=10.1021/jp907613s |issue=36}}</ref>

Full [[hydrogenation]] from both sides of the graphene sheet results in [[Graphane]], but partial hydrogenation leads to hydrogenated graphene.<ref>{{cite journal |first1=D. C. |last1=Elias |last2=Nair |first2=R. R. |last3=Mohiuddin |first3=T. M. G. |last4=Morozov |first4=S. V. |last5=Blake |first5=P. |last6=Halsall |first6=M. P. |last7=Ferrari |first7=A. C. |last8=Boukhvalov |first8=D. W. |last9=Katsnelson |first9=M. I. |last10=Geim |first10=A. K. |last11=Novoselov |first11=K. S. |title=Control of Graphene's Properties by Reversible Hydrogenation: Evidence for Graphane |journal=Science |year=2009 |volume=323 |doi=10.1126/science.1167130 |pmid=19179524 |issue=5914 |bibcode=2009Sci...323..610E |pages=610–3 |arxiv=0810.4706|s2cid=3536592 }}</ref> Similarly, both-side fluorination of graphene (or chemical and mechanical exfoliation of graphite fluoride) leads to [[fluorographene]] (graphene fluoride),<ref>{{cite journal |last1=Garcia |first1=J. C. |last2=de Lima |first2=D. B. |last3=Assali |first3=L. V. C. |last4=Justo |first4=J. F. |title=Group IV graphene- and graphane-like nanosheets |journal=J. Phys. Chem. C |date=2011 |volume=115 |issue=27 |pages=13242–13246 |doi=10.1021/jp203657w|arxiv=1204.2875 |s2cid=98682200 }}</ref> while partial fluorination (generally [[halogenation]]) provides fluorinated (halogenated) graphene.

=== Graphene ligand/complex ===

Graphene can be a [[ligand]] to [[Coordinate covalent bond|coordinate]] metals and metal ions by introducing functional groups. Structures of graphene ligands are similar to e.g. metal-[[porphyrin]] complex, metal-[[phthalocyanine]] complex, and metal-[[phenanthroline]] complex. Copper and nickel ions can be coordinated with graphene ligands.<ref>{{cite journal |doi=10.1016/j.carbon.2011.03.056 |title=Exfoliated graphene ligands stabilizing copper cations |journal=Carbon |volume=49 |issue=10 |pages=3375–3378 |year=2011 |last1=Yamada |first1=Y. |last2=Miyauchi |first2=M. |last3=Kim |first3=J. |last4=Hirose-Takai |first4=K. |last5=Sato |first5=Y. |last6=Suenaga |first6=K. |last7=Ohba |first7=T. |last8=Sodesawa |first8=T. |last9=Sato |first9=S.|bibcode=2011Carbo..49.3375Y }}<br/>{{cite journal |last1=Yamada |first1=Y. |last2=Miyauchi |first2=M. |last3=Jungpil |first3=K. |title=Exfoliated graphene ligands stabilizing copper cations |journal=Carbon |doi=10.1016/j.carbon.2011.03.056 |volume=49 |issue=10 |pages=3375–3378 |display-authors=etal|year=2011 |bibcode=2011Carbo..49.3375Y }}</ref><ref>{{cite journal |doi=10.1016/j.carbon.2014.03.036 |title=Functionalized graphene sheets coordinating metal cations |journal=Carbon |volume=75 |pages=81–94 |year=2014 |last1=Yamada |first1=Y. |last2=Suzuki |first2=Y. |last3=Yasuda |first3=H. |last4=Uchizawa |first4=S. |last5=Hirose-Takai |first5=K. |last6=Sato |first6=Y. |last7=Suenaga |first7=K. |last8=Sato |first8=S.|bibcode=2014Carbo..75...81Y }}<br/>{{cite journal |title=Functionalized graphene sheets coordinating metal cations |last1=Yamada |first1=Y. |last2=Suzuki |first2=Y. |last3=Yasuda |first3=H. |journal=Carbon |doi=10.1016/j.carbon.2014.03.036 |volume=75 |pages=81–94 |display-authors=etal|year=2014 |bibcode=2014Carbo..75...81Y }}</ref>

== Advanced graphene structures ==
=== Graphene fiber ===
In 2011, researchers reported a novel yet simple approach to fabricating graphene fibers from chemical vapor deposition-grown graphene films.<ref>{{cite journal |doi=10.1021/la202380g |pmid=21875131 |title=Directly Drawing Self-Assembled, Porous, and Monolithic Graphene Fiber from Chemical Vapor Deposition Grown Graphene Film and Its Electrochemical Properties |journal=Langmuir |volume=27 |issue=19 |pages=12164–71 |date=29 August 2011 |last1=Li |first1=Xinming |last2=Zhao |first2=Tianshuo |last3=Wang |first3=Kunlin |last4=Yang |first4=Ying |last5=Wei |first5=Jinquan |last6=Kang |first6=Feiyu |last7=Wu |first7=Dehai |last8=Zhu |first8=Hongwei |url=https://figshare.com/articles/Directly_Drawing_Self_Assembled_Porous_and_Monolithic_Graphene_Fiber_from_Chemical_Vapor_Deposition_Grown_Graphene_Film_and_Its_Electrochemical_Properties/2608015 |access-date=1 December 2019 |archive-date=1 August 2020 |archive-url=https://web.archive.org/web/20200801053549/https://figshare.com/articles/Directly_Drawing_Self_Assembled_Porous_and_Monolithic_Graphene_Fiber_from_Chemical_Vapor_Deposition_Grown_Graphene_Film_and_Its_Electrochemical_Properties/2608015 |url-status=live }}</ref> The method was scalable and controllable, delivering tunable morphology and pore structure by controlling the evaporation of solvents with suitable [[surface tension]]. Flexible all-solid-state supercapacitors based on these graphene fibers were demonstrated in 2013.<ref>{{cite journal |title=Flexible all-solid-state supercapacitors based on chemical vapor deposition derived graphene fibers |journal=Physical Chemistry Chemical Physics |volume=15 |issue=41 |pages=17752–7 |date=3 September 2013|doi=10.1039/C3CP52908H |pmid=24045695 |last1=Li |first1=Xinming |last2=Zhao |first2=Tianshuo |last3=Chen |first3=Qiao |last4=Li |first4=Peixu |last5=Wang |first5=Kunlin |last6=Zhong |first6=Minlin |last7=Wei |first7=Jinquan |last8=Wu |first8=Dehai |last9=Wei |first9=Bingqing |last10=Zhu |first10=Hongwei |s2cid=22426420 |bibcode=2013PCCP...1517752L }}</ref>

In 2015, intercalating small graphene fragments into the gaps formed by larger, coiled graphene sheets, after annealing provided pathways for conduction, while the fragments helped reinforce the fibers.{{sentence fragment |date=May 2016}} The resulting fibers offered better thermal and electrical conductivity and mechanical strength. Thermal conductivity reached {{convert|1290|W/m/K|W/m/K|abbr=in|lk=on}}, while tensile strength reached {{convert|1080|MPa|abbr=on|lk=on}}.<ref>{{Cite journal |title=Highly thermally conductive and mechanically strong graphene fibers |first1=Guoqing |last1=Xin |first2=Tiankai |last2=Yao |first3=Hongtao |last3=Sun |first4=Spencer Michael |last4=Scott |first5=Dali |last5=Shao |first6=Gongkai |last6=Wang |first7=Jie |last7=Lian |date=September 4, 2015 |journal=Science |doi=10.1126/science.aaa6502 |pmid= 26339027|volume=349 |issue=6252 |pages=1083–1087 |bibcode=2015Sci...349.1083X|doi-access=free }}</ref>

In 2016, kilometer-scale continuous graphene fibers with outstanding mechanical properties and excellent electrical conductivity were produced by high-throughput wet-spinning of graphene oxide liquid crystals followed by [[graphitization]] through a full-scale synergetic defect-engineering strategy.<ref>{{cite journal|last1= Xu|first1=Zhen|last2=Liu|first2=Yingjun|last3=Zhao|first3=Xiaoli|last4=Li|first4=Peng|last5=Sun|first5=Haiyan|last6=Xu|first6=Yang|last7=Ren|first7=Xibiao|last8=Jin|first8=Chuanhong|last9=Xu|first9=Peng|last10=Wang|first10=Miao|last11=Gao|first11=Chao|title=Ultrastiff and Strong Graphene Fibers via Full-Scale Synergetic Defect Engineering|journal= Advanced Materials|volume=28|issue=30|pages=6449–6456|date=2016|doi=10.1002/adma.201506426|pmid=27184960|bibcode=2016AdM....28.6449X |s2cid=31988847 }}</ref> The graphene fibers with superior performances promise wide applications in functional textiles, lightweight motors, microelectronic devices, etc.

[[Tsinghua University]] in Beijing, led by Wei Fei of the Department of Chemical Engineering, claims to be able to create a carbon nanotube fiber that has a tensile strength of {{convert|80|GPa|abbr=on|lk=on}}.<ref>{{cite journal|last1=Bai|first1=Yunxiang|last2=Zhang|first2=Rufan|last3=Ye|first3=Xuan|last4=Zhu|first4=Zhenxing|last5=Xie|first5=Huanhuan|last6=Shen|first6=Boyuan|last7=Cai|first7=Dali|last8=Liu|first8=Bofei|last9=Zhang|first9=Chenxi|last10=Jia|first10=Zhao|last11=Zhang|first11=Shenli|last12=Li|first12=Xide|last13=Wei|first13=Fei|date=2018|title=Carbon nanotube bundles with tensile strength over 80 GPa.|journal=Nature Nanotechnology|volume=13|issue=7|pages=589–595|doi=10.1038/s41565-018-0141-z|pmid=29760522|bibcode=2018NatNa..13..589B|s2cid=46890587}}</ref>

=== 3D graphene ===

In 2013, a three-dimensional [[honeycomb]] of hexagonally arranged carbon was termed 3D graphene, and self-supporting 3D graphene was also produced.<ref>{{cite journal |last1=Wang |first1=H. |last2=Sun |first2=K. |last3=Tao |first3=F. |last4=Stacchiola |first4=D. J. |last5=Hu |first5=Y. H. |title=3D Honeycomb-Like Structured Graphene and Its High Efficiency as a Counter-Electrode Catalyst for Dye-Sensitized Solar Cells |doi=10.1002/ange.201303497 |journal=Angewandte Chemie |volume=125 |issue=35 |pages=9380–9384 |year=2013 |pmid= 23897636|bibcode=2013AngCh.125.9380W |hdl=2027.42/99684 |hdl-access=free }}<br/>{{cite journal |url=http://www.kurzweilai.net/3d-graphene-could-replace-expensive-platinum-in-solar-cells |title=3D graphene could replace expensive platinum in solar cells |publisher=KurzweilAI |access-date=24 August 2013 |last1=Wang |first1=Hui |last2=Sun |first2=Kai |last3=Tao |first3=Franklin |last4=Stacchiola |first4=Dario J. |last5=Hu |first5=Yun Hang |journal=Angewandte Chemie |volume=125 |issue=35 |pages=9380–9384 |doi=10.1002/ange.201303497 |year=2013 |bibcode=2013AngCh.125.9380W |hdl=2027.42/99684 |hdl-access=free |archive-date=25 August 2013 |archive-url=https://web.archive.org/web/20130825023850/http://www.kurzweilai.net/3d-graphene-could-replace-expensive-platinum-in-solar-cells? |url-status=live }}</ref> 3D structures of graphene can be fabricated by using either CVD or solution-based methods. A 2016 review by Khurram and Xu et al. provided a summary of then-state-of-the-art techniques for fabrication of the 3D structure of graphene and other related two-dimensional materials.<ref name="auto">{{cite journal |last1=Shehzad |first1=Khurram |last2=Xu |first2=Yang |last3=Gao |first3=Chao |last4=Xianfeng |first4=Duan |title=Three-dimensional macro-structures of two-dimensional nanomaterials |journal=Chemical Society Reviews |volume=45 |issue=20 |pages=5541–5588 |date=2016 |doi=10.1039/C6CS00218H |pmid=27459895 }}</ref> In 2013, researchers at [[Stony Brook University]] reported a novel radical-initiated crosslinking method to fabricate porous 3D free-standing architectures of graphene and carbon nanotubes using nanomaterials as building blocks without any polymer matrix as support.<ref name="PMID 23436939">{{cite journal |last1=Lalwani |first1=Gaurav |last2=Trinward Kwaczala |first2=Andrea |last3=Kanakia |first3=Shruti |last4=Patel |first4=Sunny C. |last5=Judex |first5=Stefan |last6=Sitharaman |first6=Balaji |year=2013 |title=Fabrication and characterization of three-dimensional macroscopic all-carbon scaffolds. |journal=Carbon |volume=53 |pages=90–100 |doi=10.1016/j.carbon.2012.10.035 |pmid=23436939 |pmc=3578711}}</ref> These 3D graphenes (all-carbon) scaffolds/foams have applications in several fields such as energy storage, filtration, thermal management, and biomedical devices and implants.<ref name="auto"/><ref name="PMID 25788440">{{cite journal |last1=Lalwani |first1=Gaurav |last2=Gopalan |first2=Anu Gopalan |last3=D'Agati |first3=Michael |last4=Srinivas Sankaran |first4=Jeyantt |last5=Judex |first5=Stefan |last6=Qin |first6=Yi-Xian |last7=Sitharaman |first7=Balaji |year=2015 |title=Porous three-dimensional carbon nanotube scaffolds for tissue engineering |journal=Journal of Biomedical Materials Research Part A |volume=103 |issue=10 |pages=3212–3225 |doi=10.1002/jbm.a.35449 |pmid=25788440|pmc=4552611 }}</ref>

Box-shaped graphene (BSG) [[nanostructure]] appearing after mechanical cleavage of [[pyrolytic graphite]] was reported in 2016.<ref name="stm2016">{{cite journal |last1=Lapshin |first1=Rostislav V. |title=STM observation of a box-shaped graphene nanostructure appeared after mechanical cleavage of pyrolytic graphite |journal=Applied Surface Science |date=January 2016 |volume=360 |pages=451–460 |doi=10.1016/j.apsusc.2015.09.222 |bibcode=2016ApSS..360..451L |arxiv=1611.04379 |s2cid=119369379 }}</ref> The discovered nanostructure is a multilayer system of parallel hollow nanochannels located along the surface and having quadrangular cross-section. The thickness of the channel walls is approximately equal to 1&nbsp;nm. Potential fields of BSG application include ultra-sensitive [[detector]]s, high-performance catalytic cells, nanochannels for [[DNA]] [[sequencing]] and manipulation, high-performance heat sinking surfaces, [[rechargeable battery|rechargeable batteries]] of enhanced performance, [[nanomechanical resonator]]s, electron multiplication channels in emission [[nanoelectronics|Nano-electronic]] devices, high-capacity [[sorbent]]s for safe [[hydrogen storage]].

Three dimensional bilayer graphene has also been reported.<ref>{{cite journal |author=Harris PJF |title=Hollow structures with bilayer graphene walls |journal=Carbon |volume=50 |issue=9 |pages=3195–3199 |year=2012 |doi=10.1016/j.carbon.2011.10.050 |bibcode=2012Carbo..50.3195H |url=https://zenodo.org/record/896080 |access-date=30 August 2019 |archive-date=1 August 2020 |archive-url=https://web.archive.org/web/20200801051738/https://zenodo.org/record/896080 |url-status=live }}</ref><ref>{{cite journal |vauthors=Harris PJ, Slater TJ, Haigh SJ, Hage FS, Kepaptsoglou DM, Ramasse QM, Brydson R |title=Bilayer graphene formed by passage of current through graphite: evidence for a three dimensional structure |journal=Nanotechnology |volume=25 |issue=46 |pages=465601 |year=2014 |doi=10.1088/0957-4484/25/46/465601 |pmid=25354780 |bibcode=2014Nanot..25.5601H |s2cid=12995375 |url=http://centaur.reading.ac.uk/38041/1/3D%20FOR%20NANOTECHNOLOGY%20SUBMITTED%20REVISED%20with%20figs.pdf |access-date=30 August 2019 |archive-date=3 November 2018 |archive-url=https://web.archive.org/web/20181103103228/http://centaur.reading.ac.uk/38041/1/3D%20FOR%20NANOTECHNOLOGY%20SUBMITTED%20REVISED%20with%20figs.pdf |url-status=live }}</ref>

=== Pillared graphene ===
{{main|Pillared graphene}}

Pillared graphene is a hybrid carbon, structure consisting of an oriented array of carbon nanotubes connected at each end to a sheet of graphene. It was first described theoretically by George Froudakis and colleagues at the [[University of Crete]] in Greece in 2008. Pillared graphene has not yet been synthesized in the laboratory, but it has been suggested that it may have useful electronic properties, or as a hydrogen storage material.

=== Reinforced graphene ===

Graphene reinforced with embedded [[carbon nanotube]] reinforcing bars ("[[rebar]]") is easier to manipulate, while improving the electrical and mechanical qualities of both materials.<ref name="kurz5011">{{cite web|url=http://www.kurzweilai.net/carbon-nanotubes-as-reinforcing-bars-to-strengthen-graphene-and-increase-conductivity|title=Carbon nanotubes as reinforcing bars to strengthen graphene and increase conductivity|date=9 April 2014|publisher=Kurzweil Library|access-date=23 April 2014|archive-date=12 April 2014|archive-url=https://web.archive.org/web/20140412021444/http://www.kurzweilai.net/carbon-nanotubes-as-reinforcing-bars-to-strengthen-graphene-and-increase-conductivity|url-status=live}}</ref><ref>{{cite journal |doi=10.1021/nn501132n |pmid=24694285 |pmc=4046778 |title=Rebar Graphene |journal=ACS Nano |year=2014 |last1=Yan |first1=Z. |last2=Peng |first2=Z. |last3=Casillas |first3=G. |last4=Lin |first4=J. |last5=Xiang |first5=C. |last6=Zhou |first6=H. |last7=Yang |first7=Y. |last8=Ruan |first8=G. |last9=Raji |first9=A. R. O. |last10=Samuel |first10=E. L. G. |last11=Hauge |first11=R. H. |last12=Yacaman |first12=M. J. |last13=Tour |first13=J. M. |volume=8|issue=5 |pages=5061–8 }}</ref>

Functionalized single- or multi-walled carbon nanotubes are spin-coated on copper foils and then heated and cooled, using the nanotubes themselves as the carbon source. Under heating, the functional [[carbon group]]s decompose into graphene, while the nanotubes partially split and form in-plane [[covalent bond]]s with the graphene, adding strength. [[Pi stacking|π–π stacking]] domains add more strength. The nanotubes can overlap, making the material a better conductor than standard CVD-grown graphene. The nanotubes effectively bridge the [[grain boundary|grain boundaries]] found in conventional graphene. The technique eliminates the traces of substrate on which later-separated sheets were deposited using epitaxy.<ref name=kurz5011/>

Stacks of a few layers have been proposed as a cost-effective and physically flexible replacement for [[indium tin oxide]] (ITO) used in displays and [[photovoltaic cell]]s.<ref name=kurz5011/>

=== Molded graphene ===

In 2015, researchers from the [[University of Illinois at Urbana–Champaign|University of Illinois at Urbana-Champaign]] (UIUC) developed a new approach for forming 3D shapes from flat, 2D sheets of graphene.<ref>{{Cite web|title=Robust new process forms 3D shapes from flat sheets of graphene|url=https://grainger.illinois.edu/news/11255|date=2015-06-23|website=grainger.illinois.edu|language=en|access-date=2020-05-31|archive-date=12 May 2020|archive-url=https://web.archive.org/web/20200512144924/https://grainger.illinois.edu/news/11255|url-status=dead}}</ref> A film of graphene that had been soaked in solvent to make it swell and become malleable was overlaid on an underlying substrate "former". The solvent evaporated over time, leaving behind a layer of graphene that had taken on the shape of the underlying structure. In this way, they were able to produce a range of relatively intricate micro-structured shapes.<ref>{{cite web|url=https://newatlas.com/3d-shapes-graphene-uiuc/38164/|title=Graphene takes on a new dimension|last=Jeffrey|first=Colin|date=June 28, 2015|website=New Atlas|access-date=2019-11-10|archive-date=10 November 2019|archive-url=https://web.archive.org/web/20191110190051/https://newatlas.com/3d-shapes-graphene-uiuc/38164/|url-status=live}}</ref> Features vary from 3.5 to 50 μm. Pure graphene and gold-decorated graphene were each successfully integrated with the substrate.<ref>{{cite web|url=http://www.kurzweilai.net/how-to-form-3-d-shapes-from-flat-sheets-of-graphene|title=How to form 3-D shapes from flat sheets of graphene|date=June 30, 2015|website=Kurzweil Library|access-date=2019-11-10|archive-date=6 October 2015|archive-url=https://web.archive.org/web/20151006014133/http://www.kurzweilai.net/how-to-form-3-d-shapes-from-flat-sheets-of-graphene|url-status=live}}</ref>

== Specialized graphene configurations ==
=== Graphene aerogel ===

An [[aerogel]] made of graphene layers separated by carbon nanotubes was measured at 0.16 milligrams per cubic centimeter. A solution of graphene and carbon nanotubes in a mold is freeze-dried to dehydrate the solution, leaving the aerogel. The material has superior elasticity and absorption. It can recover completely after more than 90% compression, and absorb up to 900 times its weight in oil, at a rate of 68.8 grams per second.<ref>{{cite news |title=Graphene aerogel is seven times lighter than air, can balance on a blade of grass - Slideshow {{!}} ExtremeTech |url=http://www.extremetech.com/extreme/153063-graphene-aerogel-is-seven-times-lighter-than-air-can-balance-on-a-blade-of-grass |website=ExtremeTech |access-date=2015-10-11 |date=April 10, 2013 |first=Sebastian |last=Anthony |archive-date=8 October 2015 |archive-url=https://web.archive.org/web/20151008024745/http://www.extremetech.com/extreme/153063-graphene-aerogel-is-seven-times-lighter-than-air-can-balance-on-a-blade-of-grass |url-status=live }}</ref>

=== Graphene nanocoil ===

In 2015, a coiled form of graphene was discovered in graphitic carbon (coal). The spiraling effect is produced by defects in the material's hexagonal grid that causes it to spiral along its edge, mimicking a [[Riemann surface]], with the graphene surface approximately perpendicular to the axis. When voltage is applied to such a coil, current flows around the spiral, producing a magnetic field. The phenomenon applies to spirals with either zigzag or armchair patterns, although with different current distributions. Computer simulations indicated that a conventional spiral inductor of 205 microns in diameter could be matched by a nanocoil just 70 nanometers wide, with a field strength reaching as much as 1 [[Tesla (unit)|tesla]].<ref name=":0">{{cite web|url=http://www.kurzweilai.net/graphene-nano-coils-discovered-to-be-powerful-natural-electromagnets|title=Graphene nano-coils discovered to be powerful natural electromagnets|date=October 16, 2015|website=Kurzweil Library|access-date=2019-11-10|archive-date=19 October 2015|archive-url=https://web.archive.org/web/20151019232000/http://www.kurzweilai.net/graphene-nano-coils-discovered-to-be-powerful-natural-electromagnets?|url-status=live}}</ref>

The nano-solenoids analyzed through computer models at [[Rice University]] should be capable of producing powerful magnetic fields of about 1&nbsp;tesla, about the same as the coils found in typical loudspeakers, according to Yakobson and his team – and about the same field strength as some MRI machines. They found the magnetic field would be strongest in the hollow, nanometer-wide cavity at the spiral's center.<ref name=":0" />

A [[solenoid]] made with such a coil behaves as a quantum conductor whose current distribution between the core and exterior varies with applied voltage, resulting in nonlinear [[inductance]].<ref>{{Cite journal |title=Riemann Surfaces of Carbon as Graphene Nanosolenoids |journal=Nano Letters |volume=16 |issue=1 |pages=34–9 |date=2015-10-14 |doi=10.1021/acs.nanolett.5b02430 |pmid=26452145 |first1=Fangbo |last1=Xu |first2=Henry |last2=Yu |first3=Arta |last3=Sadrzadeh |first4=Boris I. |last4=Yakobson |bibcode=2016NanoL..16...34X}}</ref>

=== Crumpled graphene ===

In 2016, [[Brown University]] introduced a method for "crumpling" graphene, adding wrinkles to the material on a nanoscale. This was achieved by depositing layers of graphene oxide onto a shrink film, then shrunken, with the film dissolved before being shrunken again on another sheet of film. The crumpled graphene became [[Ultrahydrophobicity|superhydrophobic]], and when used as a battery electrode, the material was shown to have as much as a 400% increase in [[electrochemical]] [[current density]].<ref>{{cite web |last1=Stacey |first1=Kevin |title=Wrinkles and crumples make graphene better {{!}} News from Brown |url=https://news.brown.edu/articles/2016/03/wrinkles |website=news.brown.edu |publisher=Brown University |access-date=23 June 2016 |archive-url=https://web.archive.org/web/20160408041658/https://news.brown.edu/articles/2016/03/wrinkles |archive-date=8 April 2016 |language=en |date=21 March 2016}}</ref><ref>{{cite journal |last1=Chen |first1=Po-Yen |last2=Sodhi |first2=Jaskiranjeet |last3=Qiu |first3=Yang |last4=Valentin |first4=Thomas M. |last5=Steinberg |first5=Ruben Spitz |last6=Wang |first6=Zhongying |last7=Hurt |first7=Robert H. |last8=Wong |first8=Ian Y. |title=Multiscale Graphene Topographies Programmed by Sequential Mechanical Deformation |journal=Advanced Materials |volume=28 |issue=18 |publisher=John Wiley & Sons, Inc. |pages=3564–3571 |doi=10.1002/adma.201506194 |pmid=26996525 |date=6 May 2016|bibcode=2016AdM....28.3564C |s2cid=19544549 }}</ref>

== Mechanical synthesis ==
{{Main|Graphene production techniques}}

A rapidly increasing list of production techniques have been developed to enable graphene's use in commercial applications.<ref>{{cite journal|last1=Backes|first1=Claudia|display-authors=etal|title=Production and processing of graphene and related materials|journal=2D Materials|volume=7|pages= 022001|date=2020|issue=2|doi=10.1088/2053-1583/ab1e0a|bibcode=2020TDM.....7b2001B|doi-access=free|hdl=2262/91730|hdl-access=free}}</ref>

Isolated 2D crystals cannot be grown via chemical synthesis beyond small sizes even in principle, because the rapid growth of [[phonon]] density with increasing lateral size forces 2D crystallites to bend into the third dimension. In all cases, graphene must bond to a substrate to retain its two-dimensional shape.<ref name=geim2009a/>

=== Bottom-up and top-down methods ===
Small graphene structures, such as graphene quantum dots and nanoribbons, can be produced by "bottom-up" methods that assemble the lattice from organic molecule monomers (e. g. citric acid, glucose). "Top-down" methods, on the other hand, cut bulk graphite and graphene materials with strong chemicals (e. g. mixed acids).<ref name=":1">{{Cite journal |last1=Whitener |first1=Keith E. |last2=Sheehan |first2=Paul E. |date=2014-06-01 |title=Graphene synthesis |url=https://linkinghub.elsevier.com/retrieve/pii/S0925963514000983 |journal=Diamond and Related Materials |volume=46 |pages=25–34 |doi=10.1016/j.diamond.2014.04.006 |bibcode=2014DRM....46...25W |issn=0925-9635}}</ref>

=== Micro-mechanical cleavage ===
The most famous, clean and rather straight-forward method of isolating graphene sheets, called micro-mechanical cleavage or more colloquially called the scotch tape method, was introduced by Novoselov et al. in 2004, which uses [[adhesive tape]] to mechanically cleave high-quality [[graphite]] [[Crystal|crystals]] into successively thinner platelets. Other methods do exist like exfoliation.<ref name=":1" />

=== Exfoliation techniques ===

==== Mechanical exfoliation ====
Geim and Novoselov initially used [[adhesive tape]] to pull graphene sheets away from graphite. Achieving single layers typically requires multiple exfoliation steps. After exfoliation, the flakes are deposited on a silicon wafer. Crystallites larger than 1 mm and visible to the naked eye can be obtained.<ref name="PhysTod">{{cite journal |last1=Geim |first1=A. K. |last2=MacDonald |first2=A. H. |title=Graphene: Exploring carbon flatland |journal=Physics Today |volume=60 |pages=35–41 |year=2007 |doi=10.1063/1.2774096 |bibcode=2007PhT....60h..35G |issue=8|s2cid=123480416 |doi-access=free }}</ref>

As of 2014, exfoliation produced graphene with the lowest number of defects and highest electron mobility. Alternatively, a [[Wedge based mechanical exfoliation|sharp single-crystal diamond wedge]] can penetrate onto the graphite source to cleave layers. In the same year, defect-free, unoxidized graphene-containing liquids were made from graphite using mixers that produce local shear rates greater than {{val|10|e=4}}.<ref name="arx1406">{{cite arXiv |eprint=1406.0809 |class=cond-mat.mtrl-sci |first1=F. V. |last1=Kusmartsev |first2=W. M. |last2=Wu |title=Application of Graphene within Optoelectronic Devices and Transistors |last3=Pierpoint |first3=M. P. |last4=Yung |first4=K. C. |year=2014}}</ref><ref name="Jayasena2011">{{cite journal |last=Jayasena |first=Buddhika |author2=Subbiah Sathyan |date=2011 |title=A novel mechanical cleavage method for synthesizing few-layer graphenes |journal=Nanoscale Research Letters |volume=6 |issue=95 |pages=95 |bibcode=2011NRL.....6...95J |doi=10.1186/1556-276X-6-95 |pmc=3212245 |pmid=21711598 |doi-access=free}}</ref><ref>{{cite web |url=http://www.kurzweilai.net/a-new-method-of-producing-large-volumes-of-high-quality-graphene |title=A new method of producing large volumes of high-quality graphene |publisher=KurzweilAI |date=2 May 2014 |access-date=3 August 2014 |archive-date=10 August 2014 |archive-url=https://web.archive.org/web/20140810200204/http://www.kurzweilai.net/a-new-method-of-producing-large-volumes-of-high-quality-graphene |url-status=live }}</ref><ref>{{cite journal |doi=10.1038/nmat3944 |pmid=24747780 |title=Scalable production of large quantities of defect-free few-layer graphene by shear exfoliation in liquids |journal=Nature Materials |date=2014 |volume=13 |issue=6 |pages=624–630 |first=Keith R. |last=Paton |bibcode=2014NatMa..13..624P |hdl=2262/73941 |s2cid=43256835 |url=http://sro.sussex.ac.uk/id/eprint/84627/1/__smbhome.uscs.susx.ac.uk_akj23_Documents_Scalable%20production%20of%20large%20quantities.pdf |access-date=30 August 2019 |archive-date=7 March 2020 |archive-url=https://web.archive.org/web/20200307194908/http://sro.sussex.ac.uk/id/eprint/84627/1/__smbhome.uscs.susx.ac.uk_akj23_Documents_Scalable%20production%20of%20large%20quantities.pdf |url-status=live }}</ref>

Shear exfoliation is another method in which by using a rotor-stator mixer the scalable production of defect-free graphene has become possible. It has been shown that, as [[turbulence]] is not necessary for mechanical exfoliation, ResonantAcoustic mixing or low speed [[ball mill]]ing is effective in the production of high-yield and water-soluble graphene.<ref>{{cite journal |last1=ROUZAFZAY |first1=F. |last2=SHIDPOUR |first2=R. |year=2020 |title=Graphene@ZnO nanocompound for short-time water treatment under sun-simulated irradiation: Effect of shear exfoliation of graphene using kitchen blender on photocatalytic degradation |journal=Alloys and Compounds |volume=829 |pages=154614 |doi=10.1016/J.JALLCOM.2020.154614 |s2cid=216233251}}</ref><ref>{{cite journal |last1=Paton |first1=Keith R. |last2=Varrla |first2=Eswaraiah |last3=Backes |first3=Claudia |last4=Smith |first4=Ronan J. |last5=Khan |first5=Umar |last6=O'Neill |first6=Arlene |last7=Boland |first7=Conor |last8=Lotya |first8=Mustafa |last9=Istrate |first9=Oana M. |last10=King |first10=Paul |last11=Higgins |first11=Tom |last12=Barwich |first12=Sebastian |last13=May |first13=Peter |last14=Puczkarski |first14=Pawel |last15=Ahmed |first15=Iftikhar |date=June 2014 |title=Scalable production of large quantities of defect-free few-layer graphene by shear exfoliation in liquids |url=http://sro.sussex.ac.uk/id/eprint/84627/1/__smbhome.uscs.susx.ac.uk_akj23_Documents_Scalable%20production%20of%20large%20quantities.pdf |url-status=live |journal=Nature Materials |volume=13 |issue=6 |pages=624–630 |bibcode=2014NatMa..13..624P |doi=10.1038/nmat3944 |pmid=24747780 |s2cid=43256835 |archive-url=https://web.archive.org/web/20200307194908/http://sro.sussex.ac.uk/id/eprint/84627/1/__smbhome.uscs.susx.ac.uk_akj23_Documents_Scalable%20production%20of%20large%20quantities.pdf |archive-date=7 March 2020 |access-date=30 August 2019 |hdl-access=free |last16=Moebius |first16=Matthias |last17=Pettersson |first17=Henrik |last18=Long |first18=Edmund |last19=Coelho |first19=João |last20=O'Brien |first20=Sean E. |last21=McGuire |first21=Eva K. |last22=Sanchez |first22=Beatriz Mendoza |last23=Duesberg |first23=Georg S. |last24=McEvoy |first24=Niall |last25=Pennycook |first25=Timothy J. |last26=Downing |first26=Clive |last27=Crossley |first27=Alison |last28=Nicolosi |first28=Valeria |last29=Coleman |first29=Jonathan N. |hdl=2262/73941}}</ref><ref>{{cite patent |country=USA |number=US11038172B2 |inventor=Bor Z. Jang |status=Active |title=Environmentally benign process for producing graphene-protected anode particles for lithium batteries |pubdate=2020-09-10 |gdate=2021-06-15 |fdate=2019-03-08 |pridate=2019-03-08 |assign1=Nanotek Instruments, Inc |assign2=Global Graphene Group, Inc |url=https://patents.google.com/patent/US11038172B2/en}}</ref>

==== Liquid phase exfoliation ====
[[Liquid phase exfoliation]] (LPE) is a relatively simple method that involves dispersing graphite in a liquid medium to produce graphene by [[sonication]] or high shear mixing, followed by [[centrifugation]]. Restacking is an issue with this technique unless solvents with appropriate surface energy are used (e.g. NMP). Adding a [[surfactant]] to a solvent prior to sonication prevents restacking by adsorbing to the graphene's surface. This produces a higher graphene concentration, but removing the surfactant requires chemical treatments.<ref name="PhysTod" /><ref>{{cite journal |last1=Lotya |first1=Mustafa |last2=Hernandez |first2=Yenny |last3=King |first3=Paul J. |last4=Smith |first4=Ronan J. |last5=Nicolosi |first5=Valeria |last6=Karlsson |first6=Lisa S. |last7=Blighe |first7=Fiona M. |last8=De |first8=Sukanta |last9=Wang |first9=Zhiming |last10=McGovern |first10=I. T. |last11=Duesberg |first11=Georg S. |last12=Coleman |first12=Jonathan N. |date=18 March 2009 |title=Liquid Phase Production of Graphene by Exfoliation of Graphite in Surfactant/Water Solutions |journal=Journal of the American Chemical Society |volume=131 |issue=10 |pages=3611–3620 |arxiv=0809.2690 |doi=10.1021/ja807449u |pmid=19227978 |bibcode=2009JAChS.131.3611L |s2cid=16624132}}</ref>

LPE results in nanosheets with a broad size distribution and thicknesses roughly in the range of 1-10 monolayers. However, liquid cascade centrifugation can be used to size-select the suspensions and achieve monolayer enrichment.<ref>{{cite journal |last1=Backes |first1=Claudia |last2=Campi |first2=Davide |last3=Szydlowska |first3=Beata M. |last4=Synnatschke |first4=Kevin |last5=Ojala |first5=Ezgi |last6=Rashvand |first6=Farnia |last7=Harvey |first7=Andrew |last8=Griffin |first8=Aideen |last9=Sofer |first9=Zdenek |last10=Marzari |first10=Nicola |last11=Coleman |first11=Jonathan N. |last12=O’Regan |first12=David D. |title=Equipartition of Energy Defines the Size–Thickness Relationship in Liquid-Exfoliated Nanosheets |journal=ACS Nano |date=25 June 2019 |volume=13 |issue=6 |pages=7050–7061 |doi=10.1021/acsnano.9b02234|pmid=31199123 |arxiv=2006.14909 |s2cid=189813507 }}</ref>

Sonicating graphite at the interface of two [[Miscibility|immiscible]] liquids, most notably [[heptane]] and water, produced macro-scale graphene films. The graphene sheets are adsorbed to the high-energy interface between the materials and are kept from restacking. The sheets are up to about 95% transparent and conductive.<ref>{{cite journal |last1=Woltornist |first1=S. J. |last2=Oyer |first2=A. J. |last3=Carrillo |first3=J.-M. Y. |last4=Dobrynin |first4=A. V |last5=Adamson |first5=D. H. |s2cid=27816586 |year=2013 |title=Conductive thin films of pristine graphene by solvent interface trapping |journal=ACS Nano |volume=7 |issue=8 |pages=7062–6 |doi=10.1021/nn402371c|pmid=23879536 }}</ref>

With definite cleavage parameters, the box-shaped graphene (BSG) [[nanostructure]] can be prepared on [[graphite]] [[crystal]].<ref name="stm2016" /> A major advantage of LPE is that it can be used to exfoliate many inorganic 2D materials beyond graphene, e.g. BN, MoS2, WS2.<ref>{{cite journal |last1=Coleman |first1=Jonathan N. |last2=Lotya |first2=Mustafa |last3=O’Neill |first3=Arlene |last4=Bergin |first4=Shane D. |last5=King |first5=Paul J. |last6=Khan |first6=Umar |last7=Young |first7=Karen |last8=Gaucher |first8=Alexandre |last9=De |first9=Sukanta |last10=Smith |first10=Ronan J. |last11=Shvets |first11=Igor V. |last12=Arora |first12=Sunil K. |last13=Stanton |first13=George |last14=Kim |first14=Hye-Young |last15=Lee |first15=Kangho |last16=Kim |first16=Gyu Tae |last17=Duesberg |first17=Georg S. |last18=Hallam |first18=Toby |last19=Boland |first19=John J. |last20=Wang |first20=Jing Jing |last21=Donegan |first21=John F. |last22=Grunlan |first22=Jaime C. |last23=Moriarty |first23=Gregory |last24=Shmeliov |first24=Aleksey |last25=Nicholls |first25=Rebecca J. |last26=Perkins |first26=James M. |last27=Grieveson |first27=Eleanor M. |last28=Theuwissen |first28=Koenraad |last29=McComb |first29=David W. |last30=Nellist |first30=Peter D. |last31=Nicolosi |first31=Valeria |title=Two-Dimensional Nanosheets Produced by Liquid Exfoliation of Layered Materials |journal=Science |date=4 February 2011 |volume=331 |issue=6017 |pages=568–571 |doi=10.1126/science.1194975|pmid=21292974 |bibcode=2011Sci...331..568C |hdl=2262/66458 |s2cid=23576676 |hdl-access=free }}</ref>

==== Exfoliation with supercritical carbon dioxide ====
Liquid-phase exfoliation can also be done by a less-known process of intercalating [[supercritical carbon dioxide]] (scCO2) into the interstitial spaces in the graphite lattice, followed by rapid depressurization. The scCO2 intercalates easily inside the graphite lattice at a pressure of roughly 100 [[Atm (unit)|atm]]. Carbon dioxide turns gaseous as soon as the vessel is depressurized and makes the graphite explode into few-layered graphene.<ref name=":1" />

This method may have multiple advantages: being non-toxic, the graphite does not have to be chemically treated in any way before the process, and the whole process can be completed in a single step as opposed to other exfoliation methods.<ref name=":1" />

=== Splitting monolayer carbon allotropes ===
Graphene can be created by opening [[carbon nanotube]]s by cutting or etching.<ref>{{cite journal |title=Nanotubes cut to ribbons New techniques open up carbon tubes to create ribbons |last=Brumfiel |first=G. |journal=Nature |year=2009 |doi=10.1038/news.2009.367}}</ref> In one such method, [[MWNT|multi-walled carbon nanotubes]] were cut open in solution by action of [[potassium permanganate]] and [[sulfuric acid]].<ref>{{cite journal |title=Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons |last1=Kosynkin |first1=D. V. |last2=Higginbotham |first2=Amanda L. |last3=Sinitskii |first3=Alexander |last4=Lomeda |first4=Jay R. |last5=Dimiev |first5=Ayrat |last6=Price |first6=B. Katherine |last7=Tour |first7=James M. |journal=Nature |volume=458 |year=2009 |doi=10.1038/nature07872 |pmid=19370030 |issue=7240 |bibcode=2009Natur.458..872K |pages=872–6|hdl=10044/1/4321 |s2cid=2920478 |hdl-access=free }}</ref><ref>{{cite journal |title=Narrow graphene nanoribbons from carbon nanotubes |last1=Liying |first1=Jiao |first2=Li |last2=Zhang |first3=Xinran |last3=Wang |first4=Georgi |last4=Diankov |first5=Hongjie |last5=Dai |author-link5=Hongjie Dai |journal=Nature |volume=458 |year=2009 |doi=10.1038/nature07919 |pmid=19370031 |issue=7240 |bibcode=2009Natur.458..877J |pages=877–80|s2cid=205216466 }}</ref> In 2014, carbon nanotube-reinforced graphene was made via spin coating and annealing functionalized carbon nanotubes.<ref name="kurz5011" />

Another approach sprays [[Buckminsterfullerene|buckyballs]] at supersonic speeds onto a substrate. The balls cracked open upon impact, and the resulting unzipped cages then bond together to form a graphene film.<ref>{{cite web |title=How to Make Graphene Using Supersonic Buckyballs {{!}} MIT Technology Review |url=http://www.technologyreview.com/view/539911/how-to-make-graphene-using-supersonic-buckyballs |website=MIT Technology Review |access-date=2015-10-11 |date=August 13, 2015 |archive-date=17 December 2015 |archive-url=https://web.archive.org/web/20151217235401/http://www.technologyreview.com/view/539911/how-to-make-graphene-using-supersonic-buckyballs/ |url-status=live }}</ref>

== Chemical synthesis ==

=== Graphite oxide reduction ===
P. Boehm reported producing monolayer flakes of reduced graphene oxide in 1962.<ref name=grtim2009/><ref>{{cite web|url=http://www.aps.org/publications/apsnews/201001/letters.cfm|title=Many Pioneers in Graphene Discovery|last=Geim|first=Andre|date=January 2010|work=Letters to the Editor|publisher=American Physical Society|access-date=2019-11-10|archive-date=2 November 2021|archive-url=https://web.archive.org/web/20211102053634/https://www.aps.org/publications/apsnews/201001/letters.cfm|url-status=live}}</ref> Rapid heating of graphite oxide and exfoliation yields highly dispersed carbon powder with a few percent of graphene flakes.

Another method is the reduction of graphite oxide monolayer films, e.g. by [[hydrazine]] with [[annealing (metallurgy)|annealing]] in [[argon]]/[[hydrogen]] with an almost intact carbon framework that allows efficient removal of functional groups. Measured [[charge carrier]] mobility exceeded 1,000&nbsp;cm/Vs (10 m/Vs).<ref name="Eigler2013">{{cite journal |first1=S. |last1=Eigler |first2=M. |last2=Enzelberger-Heim |first3=S. |last3=Grimm |first4=P. |last4=Hofmann |first5=W. |last5=Kroener |first6=A. |last6=Geworski |first7=C. |last7=Dotzer |first8=M. |last8=Röckert |first9=J. |last9=Xiao |first10=C. |last10=Papp |first11=O. |last11=Lytken |first12=H.-P. |last12=Steinrück |first13=P. |last13=Müller |first14=A. |last14=Hirsch |title=Wet Chemical Synthesis of Graphene |journal=Advanced Materials |volume=25 |issue=26 |year=2013 |pages=3583–3587 |doi=10.1002/adma.201300155 |pmid=23703794|bibcode=2013AdM....25.3583E |s2cid=26172029 }}</ref>

Burning a graphite oxide coated [[DVD]] produced a conductive graphene film (1,738 siemens per meter) and specific surface area (1,520 square meters per gram) that was highly resistant and malleable.<ref>{{cite journal |title=Laser Scribing of High-Performance and Flexible Graphene-Based Electrochemical Capacitors |journal=Science |volume=335 |issue=6074 |pages=1326–1330 |date=16 March 2012 |doi=10.1126/science.1216744 |pmid=22422977 |last1=El-Kady |first1=M. F. |last2=Strong |first2=V. |last3=Dubin |first3=S. |last4=Kaner |first4=R. B. |s2cid=18958488 |bibcode=2012Sci...335.1326E }}<br/>{{cite web |last=Marcus |first=Jennifer |url=http://newsroom.ucla.edu/portal/ucla/ucla-researchers-develop-new-graphene-230478.aspx |title=Researchers develop graphene supercapacitor holding promise for portable electronics / UCLA Newsroom |publisher=Newsroom.ucla.edu |date=15 March 2012 |access-date=20 March 2012 |archive-url=https://www.webcitation.org/6HPJaTQQj?url=http://newsroom.ucla.edu/portal/ucla/ucla-researchers-develop-new-graphene-230478.aspx |archive-date=16 June 2013 |url-status=dead }}</ref>

A dispersed reduced graphene oxide suspension was synthesized in water by a hydrothermal dehydration method without using any surfactant. The approach is facile, industrially applicable, environmentally friendly, and cost-effective. Viscosity measurements confirmed that the graphene colloidal suspension (graphene nanofluid) exhibits Newtonian behavior, with the viscosity showing a close resemblance to that of water.<ref>{{cite journal |last1=Sadri |first1=R. |s2cid=53349683 |title=Experimental study on thermo-physical and rheological properties of stable and green reduced graphene oxide nanofluids: Hydrothermal assisted technique |journal=Journal of Dispersion Science and Technology |date=15 Feb 2017 |volume=38 |issue=9 |pages=1302–1310 |doi=10.1080/01932691.2016.1234387 }}</ref>

=== Molten salts ===
Graphite particles can be corroded in molten salts to form a variety of carbon nanostructures including graphene.<ref>{{cite journal |first1=A.R. |last1=Kamali |first2=D.J. |last2=Fray |journal=Carbon |volume=56 |pages=121–131 |doi=10.1016/j.carbon.2012.12.076 |title=Molten salt corrosion of graphite as a possible way to make carbon nanostructures|year=2013 |bibcode=2013Carbo..56..121K }}</ref> Hydrogen cations, dissolved in molten lithium chloride, can be discharged on cathodically-polarized graphite rods, which then intercalate, peeling graphene sheets. The graphene nanosheets produced displayed a single-crystalline structure with a lateral size of several hundred nanometers and a high degree of crystallinity and thermal stability.<ref>{{cite journal |last1=Kamali |first1=D.J.Fray |year= 2015|title=Large-scale preparation of graphene by high temperature insertion of hydrogen into graphite |journal=Nanoscale |volume=7 |issue= 26|pages=11310–11320 |doi=10.1039/C5NR01132A|pmid=26053881 |doi-access=free }}</ref>

=== Electrochemical synthesis ===
Electrochemical synthesis can exfoliate graphene. Varying a pulsed voltage controls thickness, flake area, and number of defects and affects its properties. The process begins by bathing the graphite in a solvent for intercalation. The process can be tracked by monitoring the solution's transparency with an LED and photodiode.<ref>{{cite web |title=How to tune graphene properties by introducing defects {{!}} KurzweilAI |url=http://www.kurzweilai.net/how-to-tune-graphene-properties-by-introducing-defects |website=www.kurzweilai.net |access-date=2015-10-11 |date=July 30, 2015 |archive-date=5 September 2015 |archive-url=https://web.archive.org/web/20150905200802/http://www.kurzweilai.net/how-to-tune-graphene-properties-by-introducing-defects |url-status=live }}</ref><ref>{{Cite journal |title=Controlling the properties of graphene produced by electrochemical exfoliation - IOPscience |date=2015-08-21 |doi=10.1088/0957-4484/26/33/335607 |pmid=26221914 |first1=Mario |last1=Hofmann |first2=Wan-Yu |last2=Chiang |first3=Tuân D |last3=Nguyễn |first4=Ya-Ping |last4=Hsieh |s2cid=206072084 |volume=26 |issue=33 |journal=Nanotechnology |page=335607 |bibcode=2015Nanot..26G5607H}}</ref>

=== Hydrothermal self-assembly ===
Graphene has been prepared by using a sugar like [[glucose]], [[fructose]], etc. This substrate-free "bottom-up" synthesis is safer, simpler and more environmentally friendly than exfoliation. The method can control the thickness, ranging from monolayer to multilayer, which is known as the "Tang-Lau Method".<ref name="r1">{{cite journal |last1=Tang |first1=L. |last2=Li |first2=X. |last3=Ji |first3=R. |last4=Teng |first4=K. S. |last5=Tai |first5=G. |last6=Ye |first6=J. |last7=Wei |first7=C. |last8=Lau |first8=S. P. |doi=10.1039/C2JM15944A |title=Bottom-up synthesis of large-scale graphene oxide nanosheets |journal=Journal of Materials Chemistry |volume=22 |issue=12 |page=5676 |year=2012 |hdl=10397/15682 |hdl-access=free }}</ref><ref name=lixu2013/><ref name=lili2013b/><ref name=lixu2014/>

=== Sodium ethoxide pyrolysis ===
Gram-quantities were produced by the reaction of [[ethanol]] with [[sodium]] metal, followed by [[pyrolysis]] and washing with water.<ref>{{cite journal |doi=10.1038/nnano.2008.365 |title=Gram-scale production of graphene based on solvothermal synthesis and sonication |year=2008 |last1=Choucair |first1=M. |last2=Thordarson |first2=P |last3=Stride |first3=JA |journal=Nature Nanotechnology |pmid=19119279 |volume=4 |issue=1 |pages=30–3 |bibcode=2009NatNa...4...30C}}</ref>

=== Microwave-assisted oxidation ===
In 2012, microwave energy was reported to directly synthesize graphene in one step.<ref>{{cite journal |last1=Chiu |first1=Pui Lam |last2=Mastrogiovanni |first2=Daniel D. T. |last3=Wei |first3=Dongguang |last4=Louis |first4=Cassandre |last5=Jeong |first5=Min |last6=Yu |first6=Guo |last7=Saad |first7=Peter |last8=Flach |first8=Carol R. |last9=Mendelsohn |first9=Richard |last10=Garfunkel |first10=Eric |last11=He |first11=Huixin |title=Microwave- and Nitronium Ion-Enabled Rapid and Direct Production of Highly Conductive Low-Oxygen Graphene |journal=Journal of the American Chemical Society |date=4 April 2012 |volume=134 |issue=13 |pages=5850–5856 |doi=10.1021/ja210725p |pmid=22385480 |bibcode=2012JAChS.134.5850C |s2cid=11991071 }}</ref> This approach avoids use of potassium permanganate in the reaction mixture. It was also reported that by microwave radiation assistance, graphene oxide with or without holes can be synthesized by controlling microwave time.<ref>{{cite journal |doi=10.1002/smll.201403402 |pmid=25683019 |title=Microwave Enabled One-Pot, One-Step Fabrication and Nitrogen Doping of Holey Graphene Oxide for Catalytic Applications |journal=Small |volume=11 |issue=27 |pages=3358–68 |year=2015 |last1=Patel |first1=Mehulkumar |last2=Feng |first2=Wenchun |last3=Savaram |first3=Keerthi |last4=Khoshi |first4=M. Reza |last5=Huang |first5=Ruiming |last6=Sun |first6=Jing |last7=Rabie |first7=Emann |last8=Flach |first8=Carol |last9=Mendelsohn |first9=Richard |last10=Garfunkel |first10=Eric |last11=He |first11=Huixin|s2cid=14567874 |hdl=2027.42/112245 |hdl-access=free }}</ref> Microwave heating can dramatically shorten the reaction time from days to seconds.

Graphene can also be made by [[microwave radiation|microwave]] assisted hydrothermal pyrolysis.<ref name=tang2014/><ref name=tang2012/>

=== Thermal decomposition of silicon carbide ===
Heating [[silicon carbide]] (SiC) to high temperatures ({{val|1100 |u=°C}}) under low pressures (c. 10<sup>−6</sup> torr, or 10<sup>−4</sup> Pa) reduces it to graphene.<ref name="0908.1900">{{cite journal |first1=Johannes |last1=Jobst |first2=Daniel |last2=Waldmann |first3=Florian |last3=Speck |first4=Roland |last4=Hirner |first5=Duncan K. |last5=Maude |first6=Thomas |last6=Seyller |first7=Heiko B. |last7=Weber |title=How Graphene-like is Epitaxial Graphene? Quantum Oscillations and Quantum Hall Effect |year=2009 |doi=10.1103/PhysRevB.81.195434 |journal=Physical Review B |volume=81 |issue=19 |page=195434 |arxiv=0908.1900 |bibcode=2010PhRvB..81s5434J|s2cid=118710923 }}</ref><ref name="ShenAPL">{{cite journal |first1=T. |last1=Shen |first2=J.J. |last2=Gu |first3=M |last3=Xu |first4=Y.Q. |last4=Wu |first5=M.L. |last5=Bolen |first6=M.A. |last6=Capano |first7=L.W. |last7=Engel |first8=P.D. |last8=Ye |title=Observation of quantum-Hall effect in gated epitaxial graphene grown on SiC (0001) |doi=10.1063/1.3254329 |journal=Applied Physics Letters |bibcode=2009ApPhL..95q2105S |year=2009 |volume=95 |issue=17 |page=172105 |arxiv=0908.3822|s2cid=9546283 }}</ref><ref name="0909.2903">{{cite journal |first1=Xiaosong |last1=Wu |first2=Yike |last2=Hu |first3=Ming |last3=Ruan |first4=Nerasoa K |last4=Madiomanana |first5=John |last5=Hankinson |first6=Mike |last6=Sprinkle |first7=Claire |last7=Berger |first8=Walt A. |last8=de Heer |year=2009 |title=Half integer quantum Hall effect in high mobility single layer epitaxial graphene |doi=10.1063/1.3266524 |journal=Applied Physics Letters |volume=95 |issue=22 |page=223108 |arxiv=0909.2903 |bibcode=2009ApPhL..95v3108W|s2cid=118422866 }}</ref><ref name="0909.1193">{{cite journal |first1=Samuel |last1=Lara-Avila |first2=Alexei |last2=Kalaboukhov |first3=Sara |last3=Paolillo |first4=Mikael |last4=Syväjärvi |first5=Rositza |last5=Yakimova |first6=Vladimir |last6=Fal'ko |first7=Alexander |last7=Tzalenchuk |first8=Sergey |last8=Kubatkin |title=SiC Graphene Suitable For Quantum Hall Resistance Metrology |journal=Science Brevia |date=7 July 2009 |arxiv=0909.1193 |doi=<!-- none --> |bibcode=2009arXiv0909.1193L |pmid=<!-- none -->}}</ref><ref name="phase1">{{cite journal |first1=J.A. |last1=Alexander-Webber |first2=A.M.R. |last2=Baker |first3=T.J.B.M. |last3=Janssen |first4=A. |last4=Tzalenchuk |first5=S. |last5=Lara-Avila |first6=S. |last6=Kubatkin |first7=R. |last7=Yakimova |first8=B. A. |last8=Piot |first9=D. K. |last9=Maude |first10=R.J. |last10=Nicholas |year=2013 |title=Phase Space for the Breakdown of the Quantum Hall Effect in Epitaxial Graphene |doi=10.1103/PhysRevLett.111.096601 |journal=Physical Review Letters |volume=111 |issue=9 |page=096601 |pmid=24033057 |arxiv=1304.4897 |bibcode=2013PhRvL.111i6601A|s2cid=118388086 }}</ref><ref>{{cite journal |last=Sutter |first=P. |title=Epitaxial graphene: How silicon leaves the scene |journal=Nature Materials |volume=8 |year=2009 |pmid=19229263 |doi=10.1038/nmat2392 |issue=3 |bibcode=2009NatMa...8..171S |pages=171–2 |url=https://zenodo.org/record/1233465 |access-date=12 April 2020 |archive-date=1 August 2020 |archive-url=https://web.archive.org/web/20200801050128/https://zenodo.org/record/1233465 |url-status=live }}</ref>

== Vapor deposition and growth techniques ==

=== Chemical vapor deposition ===
==== Epitaxy ====
[[Epitaxial graphene growth on silicon carbide]] is a wafer-scale technique to produce graphene. [[Epitaxy|Epitaxial]] graphene may be coupled to surfaces weakly enough (by the active valence electrons that create [[Van der Waals force]]s) to retain the two-dimensional [[electronic band structure]] of isolated graphene.<ref name=Gall1>{{cite journal |last1=Gall |first1=N. R. |last2=Rut'Kov |first2=E. V. |last3=Tontegode |first3=A. Ya. |year=1997 |title=Two Dimensional Graphite Films on Metals and Their Intercalation |journal=[[International Journal of Modern Physics B]] |volume=11 |issue=16 |pages=1865–1911 |bibcode=1997IJMPB..11.1865G |doi=10.1142/S0217979297000976}}</ref>

A normal [[silicon wafer]] coated with a layer of [[germanium]] (Ge) dipped in dilute [[hydrofluoric acid]] strips the naturally forming [[germanium oxide]] groups, creating hydrogen-terminated germanium. CVD can coat that with graphene.<ref>{{cite news |url=http://www.extremetech.com/extreme/179874-samsungs-graphene-breakthrough-could-finally-put-the-wonder-material-into-real-world-devices |title=Samsung's graphene breakthrough could finally put the wonder material into real-world devices |newspaper=ExtremeTech |date=7 April 2014 |access-date=13 April 2014 |archive-date=14 April 2014 |archive-url=https://web.archive.org/web/20140414080057/http://www.extremetech.com/extreme/179874-samsungs-graphene-breakthrough-could-finally-put-the-wonder-material-into-real-world-devices |url-status=live }}</ref><ref>{{cite journal |doi=10.1126/science.1252268 |pmid=24700471 |title=Wafer-Scale Growth of Single-Crystal Monolayer Graphene on Reusable Hydrogen-Terminated Germanium |journal=Science |volume=344 |issue=6181 |pages=286–9 |year=2014 |last1=Lee |first1=J.-H. |last2=Lee |first2=E. K. |last3=Joo |first3=W.-J. |last4=Jang |first4=Y. |last5=Kim |first5=B.-S. |last6=Lim |first6=J. Y. |last7=Choi |first7=S.-H. |last8=Ahn |first8=S. J. |last9=Ahn |first9=J. R. |last10=Park |first10=M.-H. |last11=Yang |first11=C.-W. |last12=Choi |first12=B. L. |last13=Hwang |first13=S.-W. |last14=Whang |first14=D. |bibcode=2014Sci...344..286L|s2cid=206556123 }}</ref>

The direct synthesis of graphene on insulator TiO<sub>2</sub> with high-dielectric-constant (high-κ). A two-step CVD process is shown to grow graphene directly on TiO<sub>2</sub> crystals or exfoliated TiO<sub>2</sub> nanosheets without using any metal catalyst.<ref>{{cite journal|last1=Bansal|first1=Tanesh|last2=Durcan|first2=Christopher A. |last3=Jain|first3=Nikhil|last4=Jacobs-Gedrim|first4=Robin B.|last5=Xu|first5=Yang|last6=Yu|first6=Bin|title=Synthesis of few-to-monolayer graphene on rutile titanium dioxide|journal=Carbon|volume=55|pages=168–175|date=2013|doi=10.1016/j.carbon.2012.12.023|bibcode=2013Carbo..55..168B }}</ref>

==== Metal substrates ====

CVD graphene can be grown on metal substrates including [[ruthenium]],<ref name="PhysOrg.com">{{cite news |title=A smarter way to grow graphene |url=http://www.physorg.com/news129980833.html |publisher=PhysOrg.com |date=May 2008 |access-date=11 November 2008 |archive-date=28 January 2012 |archive-url=https://web.archive.org/web/20120128134607/http://www.physorg.com/news129980833.html |url-status=live }}</ref> [[iridium]],<ref name="grIr111">{{cite journal |last1=Pletikosić |first1=I. |last2=Kralj |first2=M. |last3=Pervan |first3=P. |last4=Brako |first4=R. |last5=Coraux |first5=J. |last6=n'Diaye |first6=A. |last7=Busse |first7=C. |last8=Michely |first8=T. |year=2009 |title=Dirac Cones and Minigaps for Graphene on Ir(111) |journal=Physical Review Letters |volume=102 |page=056808 |doi=10.1103/PhysRevLett.102.056808 |pmid=19257540 |bibcode=2009PhRvL.102e6808P |issue=5 |arxiv=0807.2770|s2cid=43507175 }}</ref> [[nickel]]<ref>{{cite web |url=http://www.gizmag.com/graphene-glass-substrate-deposition/32271 |title=New process could lead to more widespread use of graphene |publisher=Gizmag.com |date=28 May 2014 |access-date=14 June 2014 |archive-date=5 September 2015 |archive-url=https://web.archive.org/web/20150905152750/http://www.gizmag.com/graphene-glass-substrate-deposition/32271/ |url-status=live }}</ref> and [[copper]].<ref>{{Cite journal|last1=Liu|first1=W.|last2=Li|first2=H.|last3=Xu|first3=C.|last4=Khatami|first4=Y.|last5=Banerjee|first5=K.|year=2011|title=Synthesis of high-quality monolayer and bilayer graphene on copper using chemical vapor deposition|url=https://www.sciencedirect.com/science/article/abs/pii/S0008622311004106|journal=Carbon|volume=49|issue=13|pages=4122–4130|doi=10.1016/j.carbon.2011.05.047|bibcode=2011Carbo..49.4122L|access-date=8 April 2020|archive-date=4 February 2021|archive-url=https://web.archive.org/web/20210204133312/https://www.sciencedirect.com/science/article/abs/pii/S0008622311004106|url-status=live}}</ref><ref>{{cite journal |last1=Mattevi |first1=Cecilia |last2=Kim |first2=Hokwon |last3=Chhowalla |first3=Manish |s2cid=213144 |title=A review of chemical vapour deposition of graphene on copper |journal=Journal of Materials Chemistry |date=2011 |volume=21 |issue=10 |pages=3324–3334 |doi=10.1039/C0JM02126A}}</ref>

==== Roll-to-roll ====

In 2014, a two-step roll-to-roll manufacturing process was announced. The first roll-to-roll step produces the graphene via chemical vapor deposition. The second step binds the graphene to a substrate.<ref>{{cite web |url=http://www.purdue.edu/newsroom/releases/2014/Q3/purdue-based-startup-scales-up-graphene-production,-develops-biosensors-and-supercapacitors.html |title=Purdue-based startup scales up graphene production, develops biosensors and supercapacitors |date=18 September 2014 |access-date=4 October 2014 |publisher=Purdue University |last=Martin |first=Steve |archive-date=3 October 2014 |archive-url=https://web.archive.org/web/20141003052536/http://www.purdue.edu/newsroom/releases/2014/Q3/purdue-based-startup-scales-up-graphene-production,-develops-biosensors-and-supercapacitors.html |url-status=live }}</ref><ref>{{Cite news |url=http://www.rdmag.com/videos/2014/09/startup-scales-graphene-production-develops-biosensors-and-supercapacitors |title=Startup scales up graphene production, develops biosensors and supercapacitors |date=19 September 2014 |work=R&D Magazine |access-date=4 October 2014 |archive-date=6 October 2014 |archive-url=https://web.archive.org/web/20141006071239/http://www.rdmag.com/videos/2014/09/startup-scales-graphene-production-develops-biosensors-and-supercapacitors |url-status=live }}</ref>
[[File:Wafer Scale CVD Graphene Raman Mapping.gif|thumb|upright=1.3|Large-area Raman mapping of CVD graphene on deposited Cu thin film on 150 mm SiO<sub>2</sub>/Si wafers reveals >95% monolayer continuity and an average value of ~2.62 for ''I''<sub>2D</sub>/''I''<sub>G</sub>. The scale bar is 200 μm.]]

==== Cold wall ====

Growing graphene in an industrial resistive-heating cold wall CVD system was claimed to produce graphene 100 times faster than conventional CVD systems, cut costs by 99%, and produce material with enhanced electronic qualities.<ref>{{cite web |title=New process could usher in "graphene-driven industrial revolution" |url=http://www.gizmag.com/graphene-low-cost-nanocvd/38195 |website=www.gizmag.com |access-date=2015-10-05 |first=Darren |last=Quick |date=June 26, 2015 |archive-date=6 September 2015 |archive-url=https://web.archive.org/web/20150906024257/http://www.gizmag.com/graphene-low-cost-nanocvd/38195/ |url-status=live }}</ref><ref>{{cite journal |last1=Bointon |first1=Thomas H. |last2=Barnes |first2=Matthew D. |last3=Russo |first3=Saverio |last4=Craciun |first4=Monica F. |author-link4=Monica Craciun |date=July 2015 |title=High Quality Monolayer Graphene Synthesized by Resistive Heating Cold Wall Chemical Vapor Deposition |journal=Advanced Materials |volume=27 |issue=28 |pages=4200–4206 |arxiv=1506.08569 |bibcode=2015AdM....27.4200B |doi=10.1002/adma.201501600 |pmc=4744682 |pmid=26053564}}</ref>

==== Wafer scale CVD graphene ====

CVD graphene is scalable and has been grown on deposited Cu thin film catalyst on 100 to 300&nbsp;mm standard Si/SiO<sub>2</sub> wafers<ref>{{Cite journal |last1=Tao |first1=Li |last2=Lee |first2=Jongho |last3=Chou |first3=Harry |last4=Holt |first4=Milo |last5=Ruoff |first5=Rodney S. |last6=Akinwande |first6=Deji |s2cid=30130350 |date=2012-03-27 |title=Synthesis of High Quality Monolayer Graphene at Reduced Temperature on Hydrogen-Enriched Evaporated Copper (111) Films |journal=ACS Nano |volume=6 |issue=3 |pages=2319–2325 |doi=10.1021/nn205068n |pmid=22314052 }}</ref><ref name=":3">{{Cite journal |last1=Tao |first1=Li |last2=Lee |first2=Jongho |last3=Holt |first3=Milo |last4=Chou |first4=Harry |last5=McDonnell |first5=Stephen J. |last6=Ferrer |first6=Domingo A. |last7=Babenco |first7=Matías G. |last8=Wallace |first8=Robert M. |last9=Banerjee |first9=Sanjay K. |s2cid=55726071 |date=2012-11-15 |title=Uniform Wafer-Scale Chemical Vapor Deposition of Graphene on Evaporated Cu (111) Film with Quality Comparable to Exfoliated Monolayer |journal=The Journal of Physical Chemistry C |volume=116 |issue=45 |pages=24068–24074 |doi=10.1021/jp3068848 }}</ref><ref name=":4">{{Cite journal |last1=Rahimi |first1=Somayyeh |last2=Tao |first2=Li |last3=Chowdhury |first3=Sk. Fahad |last4=Park |first4=Saungeun |last5=Jouvray |first5=Alex |last6=Buttress |first6=Simon |last7=Rupesinghe |first7=Nalin |last8=Teo |first8=Ken |last9=Akinwande |first9=Deji |date=2014-10-28 |title=Toward 300 mm Wafer-Scalable High-Performance Polycrystalline Chemical Vapor Deposited Graphene Transistors |journal=ACS Nano |volume=8 |issue=10 |pages=10471–10479 |doi=10.1021/nn5038493 |pmid=25198884 |s2cid=5077855 }}</ref> on an Axitron Black Magic system. Monolayer graphene coverage of >95% is achieved on 100 to 300&nbsp;mm wafer substrates with negligible defects, confirmed by extensive Raman mapping.<ref name=":3" /><ref name=":4" />

=== Solvent interface trapping method (SITM) ===

As reported by a group led by D. H. Adamson, graphene can be produced from natural graphite while preserving the integrity of the sheets using the solvent interface trapping method (SITM). SITM uses a high-energy interface, such as oil and water, to exfoliate graphite to graphene. Stacked graphite delaminates, or spreads, at the oil/water interface to produce few-layer graphene in a thermodynamically favorable process in much the same way as small molecule surfactants spread to minimize the interfacial energy. In this way, graphene behaves like a 2D surfactant.<ref>{{Cite journal |last1=Woltornist |first1=Steven J. |last2=Alamer |first2=Fahad Alhashmi |last3=McDannald |first3=Austin |last4=Jain |first4=Menka |last5=Sotzing |first5=Gregory A. |last6=Adamson |first6=Douglas H. |date=2015-01-01 |title=Preparation of conductive graphene/graphite infused fabrics using an interface trapping method |url=https://www.sciencedirect.com/science/article/pii/S0008622314008719 |journal=Carbon |language=en |volume=81 |pages=38–42 |doi=10.1016/j.carbon.2014.09.020 |bibcode=2015Carbo..81...38W |issn=0008-6223}}</ref><ref>{{Cite journal |last1=Woltornist |first1=Steven J. |last2=Carrillo |first2=Jan-Michael Y. |last3=Xu |first3=Thomas O. |last4=Dobrynin |first4=Andrey V. |last5=Adamson |first5=Douglas H. |date=2015-02-10 |title=Polymer/Pristine Graphene Based Composites: From Emulsions to Strong, Electrically Conducting Foams |url=https://pubs.acs.org/doi/10.1021/ma5024236 |journal=Macromolecules |language=en |volume=48 |issue=3 |pages=687–693 |doi=10.1021/ma5024236 |bibcode=2015MaMol..48..687W |osti=1265313 |issn=0024-9297 |access-date=13 July 2022 |archive-date=13 July 2022 |archive-url=https://web.archive.org/web/20220713200603/https://pubs.acs.org/doi/10.1021/ma5024236 |url-status=live }}</ref><ref>{{Cite journal |last1=Ward |first1=Shawn P. |last2=Abeykoon |first2=Prabodha G. |last3=McDermott |first3=Sean T. |last4=Adamson |first4=Douglas H. |date=2020-09-08 |title=Effect of Aqueous Anions on Graphene Exfoliation |url=https://pubs.acs.org/doi/10.1021/acs.langmuir.0c01569 |journal=Langmuir |language=en |volume=36 |issue=35 |pages=10421–10428 |doi=10.1021/acs.langmuir.0c01569 |pmid=32794716 |s2cid=225385130 |issn=0743-7463 |access-date=13 July 2022 |archive-date=13 July 2022 |archive-url=https://web.archive.org/web/20220713200601/https://pubs.acs.org/doi/10.1021/acs.langmuir.0c01569 |url-status=live }}</ref> SITM has been reported for a variety of applications such conductive polymer-graphene foams,<ref>{{Cite journal |last1=Bento |first1=Jennifer L. |last2=Brown |first2=Elizabeth |last3=Woltornist |first3=Steven J. |last4=Adamson |first4=Douglas H. |date=January 2017 |title=Thermal and Electrical Properties of Nanocomposites Based on Self-Assembled Pristine Graphene |journal=Advanced Functional Materials |language=en |volume=27 |issue=1 |pages=1604277 |doi=10.1002/adfm.201604277 |s2cid=102395615 |issn=1616-301X|doi-access=free }}</ref><ref>{{Cite journal |last1=Woltornist |first1=Steven J. |last2=Varghese |first2=Deepthi |last3=Massucci |first3=Daniel |last4=Cao |first4=Zhen |last5=Dobrynin |first5=Andrey V. |last6=Adamson |first6=Douglas H. |date=May 2017 |title=Controlled 3D Assembly of Graphene Sheets to Build Conductive, Chemically Selective and Shape-Responsive Materials |url=https://onlinelibrary.wiley.com/doi/10.1002/adma.201604947 |journal=Advanced Materials |language=en |volume=29 |issue=18 |pages=1604947 |doi=10.1002/adma.201604947 |pmid=28262992 |bibcode=2017AdM....2904947W |s2cid=205274548 |issn=0935-9648 |access-date=13 July 2022 |archive-date=13 July 2022 |archive-url=https://web.archive.org/web/20220713200600/https://onlinelibrary.wiley.com/doi/10.1002/adma.201604947 |url-status=live }}</ref><ref>{{Cite journal |last1=Varghese |first1=Deepthi |last2=Bento |first2=Jennifer L. |last3=Ward |first3=Shawn P. |last4=Adamson |first4=Douglas H. |date=2020-06-16 |title=Self-Assembled Graphene Composites for Flow-Through Filtration |url=https://pubs.acs.org/doi/10.1021/acsami.0c05831 |journal=ACS Applied Materials & Interfaces |volume=12 |issue=26 |language=en |pages=29692–29699 |doi=10.1021/acsami.0c05831 |pmid=32492330 |s2cid=219316507 |issn=1944-8244 |access-date=13 July 2022 |archive-date=13 July 2022 |archive-url=https://web.archive.org/web/20220713200604/https://pubs.acs.org/doi/10.1021/acsami.0c05831 |url-status=live }}</ref><ref>{{Cite journal |last1=Brown |first1=Elizabeth E. B. |last2=Woltornist |first2=Steven J. |last3=Adamson |first3=Douglas H. |date=2020-11-15 |title=PolyHIPE foams from pristine graphene: Strong, porous, and electrically conductive materials templated by a 2D surfactant |url=https://www.sciencedirect.com/science/article/pii/S0021979720309048 |journal=Journal of Colloid and Interface Science |language=en |volume=580 |pages=700–708 |doi=10.1016/j.jcis.2020.07.026 |pmid=32712476 |bibcode=2020JCIS..580..700B |s2cid=220798190 |issn=0021-9797}}</ref> conductive polymer-graphene microspheres,<ref>{{Cite journal |last1=Liyanage |first1=Chinthani D. |last2=Varghese |first2=Deepthi |last3=Brown |first3=Elizabeth E. B. |last4=Adamson |first4=Douglas H. |date=2019-11-05 |title=Pristine Graphene Microspheres by the Spreading and Trapping of Graphene at an Interface |url=https://pubs.acs.org/doi/10.1021/acs.langmuir.9b02650 |journal=Langmuir |language=en |volume=35 |issue=44 |pages=14310–14315 |doi=10.1021/acs.langmuir.9b02650 |pmid=31647673 |s2cid=204883163 |issn=0743-7463 |access-date=13 July 2022 |archive-date=13 July 2022 |archive-url=https://web.archive.org/web/20220713200601/https://pubs.acs.org/doi/10.1021/acs.langmuir.9b02650 |url-status=live }}</ref> conductive thin films<ref>{{Cite journal |last1=Woltornist |first1=Steven J. |last2=Oyer |first2=Andrew J. |last3=Carrillo |first3=Jan-Michael Y. |last4=Dobrynin |first4=Andrey V. |last5=Adamson |first5=Douglas H. |date=2013-08-27 |title=Conductive Thin Films of Pristine Graphene by Solvent Interface Trapping |url=https://pubs.acs.org/doi/10.1021/nn402371c |journal=ACS Nano |language=en |volume=7 |issue=8 |pages=7062–7066 |doi=10.1021/nn402371c |pmid=23879536 |issn=1936-0851 |access-date=13 July 2022 |archive-date=13 July 2022 |archive-url=https://web.archive.org/web/20220713200605/https://pubs.acs.org/doi/10.1021/nn402371c |url-status=live }}</ref> and conductive inks.<ref>{{Cite journal |last1=Chen |first1=Feiyang |last2=Varghese |first2=Deepthi |last3=McDermott |first3=Sean T. |last4=George |first4=Ian |last5=Geng |first5=Lijiang |last6=Adamson |first6=Douglas H. |date=2020-10-22 |title=Interface-exfoliated graphene-based conductive screen-printing inks: low-loading, low-cost, and additive-free |journal=Scientific Reports |language=en |volume=10 |issue=1 |pages=18047 |doi=10.1038/s41598-020-74821-3 |pmid=33093555 |pmc=7583245 |bibcode=2020NatSR..1018047C |issn=2045-2322}}</ref>

=== Carbon dioxide reduction ===

A highly exothermic reaction combusts [[magnesium]] in an oxidation-reduction reaction with carbon dioxide, producing carbon nanoparticles including graphene and [[fullerene]]s.<ref>{{Cite journal |last1=Chakrabarti |first1=A. |last2=Lu |first2=J. |last3=Skrabutenas |first3=J. C. |last4=Xu |first4=T. |last5=Xiao |first5=Z. |last6=Maguire |first6=J. A. |last7=Hosmane |first7=N. S. |s2cid=96850993 |doi=10.1039/C1JM11227A |title=Conversion of carbon dioxide to few-layer graphene |journal=Journal of Materials Chemistry |volume=21 |issue=26 |page=9491 |year=2011 }}</ref>

=== Supersonic spray ===

Supersonic acceleration of droplets through a [[Laval nozzle]] was used to deposit reduced graphene oxide on a substrate. The energy of the impact rearranges those carbon atoms into flawless graphene.<ref>{{Cite journal |doi=10.1002/adfm.201400732 |title=Self-Healing Reduced Graphene Oxide Films by Supersonic Kinetic Spraying |journal=Advanced Functional Materials |volume=24 |issue=31 |pages=4986–4995 |year=2014 |last1=Kim |first1=D. Y. |last2=Sinha-Ray |first2=S. |last3=Park |first3=J. J. |last4=Lee |first4=J. G. |last5=Cha |first5=Y. H. |last6=Bae |first6=S. H. |last7=Ahn |first7=J. H. |last8=Jung |first8=Y. C. |last9=Kim |first9=S. M. |last10=Yarin |first10=A. L. |last11=Yoon |first11=S. S.|s2cid=96283118 }}</ref><ref>{{cite journal |url=http://www.kurzweilai.net/supersonic-spray-creates-high-quality-graphene-layer |title=Supersonic spray creates high-quality graphene layer |journal=Advanced Functional Materials |volume=24 |issue=31 |pages=4986–4995 |doi=10.1002/adfm.201400732 |publisher=KurzweilAI |access-date=14 June 2014 |year=2014 |last1=Kim |first1=Do-Yeon |last2=Sinha-Ray |first2=Suman |last3=Park |first3=Jung-Jae |last4=Lee |first4=Jong-Gun |last5=Cha |first5=You-Hong |last6=Bae |first6=Sang-Hoon |last7=Ahn |first7=Jong-Hyun |last8=Jung |first8=Yong Chae |last9=Kim |first9=Soo Min |last10=Yarin |first10=Alexander L. |last11=Yoon |first11=Sam S. |s2cid=96283118 |archive-date=4 June 2014 |archive-url=https://web.archive.org/web/20140604000811/http://www.kurzweilai.net/supersonic-spray-creates-high-quality-graphene-layer |url-status=live }}</ref>

=== Laser ===

In 2014, a {{chem|CO|2}} [[infrared laser]] was used to produce patterned porous three-dimensional laser-induced graphene (LIG) film networks from commercial polymer films. The resulting material exhibits high electrical conductivity and surface area. The laser induction process is compatible with roll-to-roll manufacturing processes.<ref>{{Cite journal |doi=10.1038/ncomms6714 |pmid=25493446 |pmc=4264682 |title=Laser-induced porous graphene films from commercial polymers |journal=Nature Communications |volume=5 |page=5714 |year=2014 |last1=Lin |first1=J. |last2=Peng |first2=Z. |last3=Liu |first3=Y. |last4=Ruiz-Zepeda |first4=F. |last5=Ye |first5=R. |last6=Samuel |first6=E. L. G. |last7=Yacaman |first7=M. J. |last8=Yakobson |first8=B. I. |last9=Tour |first9=J. M. |bibcode=2014NatCo...5.5714L}}</ref> A similar material, laser-induced graphene fibers (LIGF), was reported in 2018.<ref>{{Cite journal|last1=Duy|first1=Luong Xuan|last2=Peng|first2=Zhiwei|last3=Li|first3=Yilun|last4=Zhang|first4=Jibo|last5=Ji|first5=Yongsung|last6=Tour|first6=James M.|date=2018-01-01|title=Laser-induced graphene fibers|url=https://www.sciencedirect.com/science/article/pii/S0008622317310370|journal=Carbon|language=en|volume=126|pages=472–479|doi=10.1016/j.carbon.2017.10.036|bibcode=2018Carbo.126..472D |issn=0008-6223}}</ref>

=== Flash Joule heating ===

In 2019, flash Joule heating (transient high-temperature electrothermal heating) was discovered to be a method to synthesize turbostratic graphene in bulk powder form. The method involves electrothermally converting various carbon sources, such as carbon black, coal, and food waste into micron-scale flakes of graphene.<ref name="Luong 647–651"/><ref>{{Cite journal|last1=Stanford|first1=Michael G.|last2=Bets|first2=Ksenia V.|last3=Luong|first3=Duy X.|last4=Advincula|first4=Paul A.|last5=Chen|first5=Weiyin|last6=Li|first6=John Tianci|last7=Wang|first7=Zhe|last8=McHugh|first8=Emily A.|last9=Algozeeb|first9=Wala A.|last10=Yakobson|first10=Boris I.|last11=Tour|first11=James M.|date=2020-10-27|title=Flash Graphene Morphologies|url=https://pubs.acs.org/doi/10.1021/acsnano.0c05900|journal=ACS Nano|language=en|volume=14|issue=10|pages=13691–13699|doi=10.1021/acsnano.0c05900|pmid=32909736|osti=1798502|s2cid=221623214|issn=1936-0851|access-date=16 October 2021|archive-date=4 August 2022|archive-url=https://web.archive.org/web/20220804211511/https://pubs.acs.org/doi/10.1021/acsnano.0c05900|url-status=live}}</ref> More recent works demonstrated the use of mixed [[plastic waste]], waste rubber tires, and pyrolysis ash as carbon feedstocks.<ref>{{Cite journal|last1=Algozeeb|first1=Wala A.|last2=Savas|first2=Paul E.|last3=Luong|first3=Duy Xuan|last4=Chen|first4=Weiyin|last5=Kittrell|first5=Carter|last6=Bhat|first6=Mahesh|last7=Shahsavari|first7=Rouzbeh|last8=Tour|first8=James M.|date=2020-11-24|title=Flash Graphene from Plastic Waste|url=https://pubs.acs.org/doi/10.1021/acsnano.0c06328|journal=ACS Nano|language=en|volume=14|issue=11|pages=15595–15604|doi=10.1021/acsnano.0c06328|pmid=33119255|osti=1798504|s2cid=226203667|issn=1936-0851|access-date=16 October 2021|archive-date=16 October 2021|archive-url=https://web.archive.org/web/20211016050155/https://pubs.acs.org/doi/10.1021/acsnano.0c06328|url-status=live}}</ref><ref>{{Cite journal|last1=Wyss|first1=Kevin M.|last2=Beckham|first2=Jacob L.|last3=Chen|first3=Weiyin|last4=Luong|first4=Duy Xuan|last5=Hundi|first5=Prabhas|last6=Raghuraman|first6=Shivaranjan|last7=Shahsavari|first7=Rouzbeh|last8=Tour|first8=James M.|date=2021-04-15|title=Converting plastic waste pyrolysis ash into flash graphene|journal=Carbon|language=en|volume=174|pages=430–438|doi=10.1016/j.carbon.2020.12.063|s2cid=232864412|issn=0008-6223|doi-access=free|bibcode=2021Carbo.174..430W }}</ref><ref>{{Cite journal|last1=Advincula|first1=Paul A.|last2=Luong|first2=Duy Xuan|last3=Chen|first3=Weiyin|last4=Raghuraman|first4=Shivaranjan|last5=Shahsavari|first5=Rouzbeh|last6=Tour|first6=James M.|date=June 2021|title=Flash graphene from rubber waste|journal=Carbon|language=en|volume=178|pages=649–656|doi=10.1016/j.carbon.2021.03.020|s2cid=233573678|issn=0008-6223|doi-access=free|bibcode=2021Carbo.178..649A }}</ref> The graphenization process is kinetically controlled, and the energy dose is chosen to preserve the carbon in its graphenic state (excessive energy input leads to subsequent graphitization through annealing).

=== Ion implantation ===

Accelerating carbon ions inside an electrical field into a semiconductor made of thin nickel films on a substrate of SiO<sub>2</sub>/Si, creates a wafer-scale ({{Convert|4|in}}) wrinkle/tear/residue-free graphene layer at a relatively low temperature of 500&nbsp;°C.<ref>{{cite web |title=Korean researchers grow wafer-scale graphene on a silicon substrate {{!}} KurzweilAI |url=http://www.kurzweilai.net/korean-researchers-grow-wafer-scale-graphene-on-a-silicon-substrate |website=www.kurzweilai.net |access-date=2015-10-11 |date=July 21, 2015 |archive-date=7 August 2020 |archive-url=https://web.archive.org/web/20200807051259/https://www.kurzweilai.net/korean-researchers-grow-wafer-scale-graphene-on-a-silicon-substrate |url-status=live }}</ref><ref>{{cite journal |last1=Kim |first1=Janghyuk |last2=Lee |first2=Geonyeop |last3=Kim |first3=Jihyun |title=Wafer-scale synthesis of multi-layer graphene by high-temperature carbon ion implantation |journal=Applied Physics Letters |date=20 July 2015 |volume=107 |issue=3 |pages=033104 |doi=10.1063/1.4926605 |bibcode=2015ApPhL.107c3104K }}</ref>

=== CMOS-compatible graphene ===

Integration of graphene in the widely employed [[Semiconductor device fabrication|CMOS fabrication process]] demands its transfer-free direct synthesis on [[dielectric]] substrates at temperatures below 500 °C. At the [[International Electron Devices Meeting|IEDM]] 2018, researchers from [[University of California, Santa Barbara]], demonstrated a novel CMOS-compatible graphene synthesis process at 300&nbsp;°C suitable for back-end-of-line ([[Back end of line|BEOL]]) applications.<ref>{{Cite journal|last=Thomas|first=Stuart|date=2018|title=CMOS-compatible graphene|journal=Nature Electronics|volume=1|issue=12|pages=612|doi=10.1038/s41928-018-0178-x|s2cid=116643404|doi-access=free}}</ref><ref>{{cite book |doi=10.1109/IEDM.2018.8614535 |chapter=CMOS-Compatible Doped-Multilayer-Graphene Interconnects for Next-Generation VLSI |title=2018 IEEE International Electron Devices Meeting (IEDM) |year=2018 |last1=Jiang |first1=Junkai |last2=Chu |first2=Jae Hwan |last3=Banerjee |first3=Kaustav |author3-link=Kaustav Banerjee |pages=34.5.1–34.5.4 |isbn=978-1-7281-1987-8 |s2cid=58675631 }}</ref><ref>{{Cite news|url=https://www.news.ucsb.edu/2019/019563/graphene-goes-mainstream|title=Graphene goes mainstream|date=July 23, 2019|work=The Current, UC Santa Barbara|access-date=9 April 2020|archive-date=1 August 2020|archive-url=https://web.archive.org/web/20200801101103/https://www.news.ucsb.edu/2019/019563/graphene-goes-mainstream|url-status=live}}</ref> The process involves pressure-assisted solid-state [[diffusion]] of [[carbon]] through a [[Thin film|thin-film]] of metal catalyst. The synthesized large-area graphene films were shown to exhibit high quality (via [[Raman spectroscopy|Raman]] characterization) and similar [[Electrical resistivity and conductivity|resistivity]] values when compared with high-temperature CVD synthesized graphene films of the same cross-section down to widths of 20 [[Nanometre|nm]].

== Simulation ==

In addition to experimental investigation of graphene and graphene-based devices, numerical modeling and simulation of graphene has also been an important research topic. The [[Kubo formula]] provides an analytic expression for the graphene's conductivity and shows that it is a function of several physical parameters including wavelength, temperature, and chemical potential.<ref>{{cite journal |last1=Gusynin |first1=V P |last2=Sharapov |first2=S G |last3=Carbotte |first3=J P |title=Magneto-optical conductivity in graphene |journal=Journal of Physics: Condensed Matter |date=17 January 2007 |volume=19 |issue=2 |pages=026222 |doi=10.1088/0953-8984/19/2/026222|arxiv=0705.3783 |bibcode=2007JPCM...19b6222G |s2cid=119638159 }}</ref> Moreover, a surface conductivity model, which describes graphene as an infinitesimally thin (two-sided) sheet with a local and isotropic conductivity, has been proposed. This model permits the derivation of analytical expressions for the electromagnetic field in the presence of a graphene sheet in terms of a dyadic Green function (represented using Sommerfeld integrals) and exciting electric current.<ref>{{cite journal |last1=Hanson |first1=George W. |title=Dyadic Green's Functions for an Anisotropic, Non-Local Model of Biased Graphene |journal=IEEE Transactions on Antennas and Propagation |date=March 2008 |volume=56 |issue=3 |pages=747–757 |doi=10.1109/TAP.2008.917005|bibcode=2008ITAP...56..747H |s2cid=32535262 }}</ref>

Even though these analytical models and methods can provide results for several canonical problems for benchmarking purposes, many practical problems involving graphene, such as the design of arbitrarily shaped electromagnetic devices, are analytically intractable. With the recent advances in the field of [[Computational electromagnetics|computational electromagnetics (CEM)]], various accurate and efficient numerical methods have become available for analysis of electromagnetic field/wave interactions on graphene sheets and/or graphene-based devices. A comprehensive summary of computational tools developed for analyzing graphene-based devices/systems is proposed.<ref>{{cite journal |last1=Niu |first1=Kaikun |last2=Li |first2=Ping |last3=Huang |first3=Zhixiang |last4=Jiang |first4=Li Jun |last5=Bagci |first5=Hakan |title=Numerical Methods for Electromagnetic Modeling of Graphene: A Review |journal=[[IEEE Journal on Multiscale and Multiphysics Computational Techniques]] |date=2020 |volume=5 |pages=44–58 |doi=10.1109/JMMCT.2020.2983336 |bibcode=2020IJMMC...5...44N |hdl=10754/662399 |s2cid=216262889 |hdl-access=free }}</ref>

== Graphene analogs ==

Graphene analogs<ref>{{cite journal |last1=Polini |first1=Marco |last2=Guinea |first2=Francisco |last3=Lewenstein |first3=Maciej |last4=Manoharan |first4=Hari C. |last5=Pellegrini |first5=Vittorio |title=Artificial honeycomb lattices for electrons, atoms and photons |journal=Nature Nanotechnology |date=September 2013 |volume=8 |issue=9 |pages=625–633 |doi=10.1038/nnano.2013.161 |pmid=24002076 |arxiv=1304.0750 |bibcode=2013NatNa...8..625P }}</ref> (also referred to as "artificial graphene") are two-dimensional systems which exhibit similar properties to graphene. Graphene analogs have been studied intensively since the discovery of graphene in 2004. People try to develop systems in which the physics is easier to observe and manipulate than in graphene. In those systems, electrons are not always the particles that are used. They might be optical photons,<ref>{{cite journal |last1=Plotnik |first1=Yonatan |last2=Rechtsman |first2=Mikael C. |last3=Song |first3=Daohong |last4=Heinrich |first4=Matthias |last5=Zeuner |first5=Julia M. |last6=Nolte |first6=Stefan |last7=Lumer |first7=Yaakov |last8=Malkova |first8=Natalia |last9=Xu |first9=Jingjun |last10=Szameit |first10=Alexander |last11=Chen |first11=Zhigang |last12=Segev |first12=Mordechai |title=Observation of unconventional edge states in 'photonic graphene' |journal=Nature Materials |date=January 2014 |volume=13 |issue=1 |pages=57–62 |doi=10.1038/nmat3783 |pmid=24193661 |bibcode=2014NatMa..13...57P |arxiv=1210.5361 |s2cid=26962706 }}</ref> microwave photons,<ref>{{Cite journal |title=Topological Transition of Dirac Points in a Microwave Experiment |journal=Physical Review Letters |date=2013-01-14 |page=033902 |volume=110 |issue=3 |doi=10.1103/PhysRevLett.110.033902 |pmid=23373925 |first1=Matthieu |last1=Bellec |first2=Ulrich |last2=Kuhl |first3=Gilles |last3=Montambaux |first4=Fabrice |last4=Mortessagne |arxiv=1210.4642 |bibcode=2013PhRvL.110c3902B|s2cid=8335461 }}</ref> plasmons,<ref>{{cite journal |last1=Scheeler |first1=Sebastian P. |last2=Mühlig |first2=Stefan |last3=Rockstuhl |first3=Carsten |last4=Hasan |first4=Shakeeb Bin |last5=Ullrich |first5=Simon |last6=Neubrech |first6=Frank |last7=Kudera |first7=Stefan |last8=Pacholski |first8=Claudia |title=Plasmon Coupling in Self-Assembled Gold Nanoparticle-Based Honeycomb Islands |journal=The Journal of Physical Chemistry C |date=12 September 2013 |volume=117 |issue=36 |pages=18634–18641 |doi=10.1021/jp405560t }}</ref> microcavity polaritons,<ref>{{Cite journal |title=Direct Observation of Dirac Cones and a Flatband in a Honeycomb Lattice for Polaritons |journal=Physical Review Letters |date=2014-03-18 |page=116402 |volume=112 |issue=11 |doi=10.1103/PhysRevLett.112.116402 |pmid=24702392 |first1=T. |last1=Jacqmin |first2=I. |last2=Carusotto |first3=I. |last3=Sagnes |first4=M. |last4=Abbarchi |first5=D. D. |last5=Solnyshkov |first6=G. |last6=Malpuech |first7=E. |last7=Galopin |first8=A. |last8=Lemaître |first9=J. |last9=Bloch |arxiv=1310.8105 |bibcode=2014PhRvL.112k6402J|s2cid=31526933 }}</ref> or even atoms.<ref>{{cite journal |title= Multi-component quantum gases in spin-dependent hexagonal lattices|issue=5 |pages=434–440 |journal=Nature Physics |volume=7 |doi=10.1038/nphys1916 |date=May 2011 |last1=Sengstock |first1=K. |last2=Lewenstein |first2=M. |last3=Windpassinger |first3=P. |last4=Becker |first4=C. |last5=Meineke |first5=G. |last6=Plenkers |first6=W. |last7=Bick |first7=A. |last8=Hauke |first8=P. |last9=Struck |first9=J. |last10=Soltan-Panahi |first10=P. |bibcode=2011NatPh...7..434S |arxiv=1005.1276 |s2cid=118519844 }}</ref> Also, the honeycomb structure in which those particles evolve can be of a different nature than carbon atoms in graphene. It can be, respectively, a [[photonic crystal]], an array of metallic rods, metallic [[nanoparticle]]s, a lattice of coupled microcavities, or an [[optical lattice]].

== Applications ==
{{main|Potential applications of graphene}}

Graphene is a transparent and flexible conductor that holds great promise for various material/device applications, including solar cells,<ref>{{cite journal |last1=Zhong |first1=Mengyao |last2=Xu |first2=Dikai |last3=Yu |first3=Xuegong |last4=Huang |first4=Kun |last5=Liu |first5=Xuemei |last6=Qu |first6=Yiming |last7=Xu |first7=Yang |last8=Yang |first8=Deren |title=Interface coupling in graphene/fluorographene heterostructure for high-performance graphene/silicon solar cells |journal=Nano Energy |date=October 2016 |volume=28 |pages=12–18 |doi=10.1016/j.nanoen.2016.08.031 |bibcode=2016NEne...28...12Z }}</ref> light-emitting diodes (LED), integrated photonic circuit devices,<ref>{{Cite journal |last1=Phare |first1=Christopher T. |last2=Daniel Lee |first2=Yoon-Ho |last3=Cardenas |first3=Jaime |last4=Lipson |first4=Michal |year=2015 |title=Graphene electro-optic modulator with 30 GHz bandwidth |url=https://www.nature.com/articles/nphoton.2015.122 |journal=Nature Photonics |language=en |volume=9 |issue=8 |pages=511–514 |doi=10.1038/nphoton.2015.122 |bibcode=2015NaPho...9..511P |s2cid=117786282 |issn=1749-4893 |access-date=19 September 2022 |archive-date=24 September 2022 |archive-url=https://web.archive.org/web/20220924083922/https://www.nature.com/articles/nphoton.2015.122 |url-status=live }}</ref><ref>{{Cite journal |last1=Meng |first1=Yuan |last2=Ye |first2=Shengwei |last3=Shen |first3=Yijie |last4=Xiao |first4=Qirong |last5=Fu |first5=Xing |last6=Lu |first6=Rongguo |last7=Liu |first7=Yong |last8=Gong |first8=Mali |year=2018 |title=Waveguide Engineering of Graphene Optoelectronics—Modulators and Polarizers |journal=IEEE Photonics Journal |volume=10 |issue=1 |pages=1–17 |doi=10.1109/JPHOT.2018.2789894 |bibcode=2018IPhoJ..1089894M |s2cid=25707442 |issn=1943-0655|doi-access=free }}</ref> touch panels, and smart windows or phones.<ref>{{Cite journal |last1=Akinwande |first1=D. |last2=Tao |first2=L. |last3=Yu |first3=Q. |last4=Lou |first4=X. |last5=Peng |first5=P. |last6=Kuzum |first6=D. |author-link6=Duygu Kuzum |date=2015-09-01 |title=Large-Area Graphene Electrodes: Using CVD to facilitate applications in commercial touchscreens, flexible nanoelectronics, and neural interfaces. |journal=IEEE Nanotechnology Magazine |volume=9 |issue=3 |pages=6–14 |doi=10.1109/MNANO.2015.2441105 |s2cid=26541191}}</ref> Smartphone products with graphene touch screens are already on the market.<ref>{{Cite journal |last1=Kong |first1=Wei |last2=Kum |first2=Hyun |last3=Bae |first3=Sang-Hoon |last4=Shim |first4=Jaewoo |last5=Kim |first5=Hyunseok |last6=Kong |first6=Lingping |last7=Meng |first7=Yuan |last8=Wang |first8=Kejia |last9=Kim |first9=Chansoo |last10=Kim |first10=Jeehwan |year=2019 |title=Path towards graphene commercialization from lab to market |url=https://www.nature.com/articles/s41565-019-0555-2 |journal=Nature Nanotechnology |language=en |volume=14 |issue=10 |pages=927–938 |doi=10.1038/s41565-019-0555-2 |pmid=31582831 |bibcode=2019NatNa..14..927K |s2cid=203653990 |issn=1748-3395 |access-date=17 September 2022 |archive-date=22 September 2022 |archive-url=https://web.archive.org/web/20220922232818/https://www.nature.com/articles/s41565-019-0555-2 |url-status=live }}</ref>

In 2013, Head announced their new range of graphene tennis racquets.<ref>{{Cite news|url=http://www.tennis.com/gear/2015/02/racquet-review-head-graphene-xt-speed-pro/53947/|title=Racquet Review: Head Graphene XT Speed Pro|newspaper=Tennis.com|access-date=2016-10-15|archive-date=2 May 2019|archive-url=https://web.archive.org/web/20190502064716/http://www.tennis.com/gear/2015/02/racquet-review-head-graphene-xt-speed-pro/53947/|url-status=live}}</ref>

As of 2015, there is one product available for commercial use: a graphene-infused printer powder.<ref>{{cite web |url=https://www.noble3dprinters.com/product/graphenite-graphene-infused-3d-printer-powder-30-lbs-499-95 |archive-url=https://web.archive.org/web/20231109153237/https://www.noble3dprinters.com/product/graphenite-graphene-infused-3d-printer-powder-30-lbs-499-95 |url-status=dead |archive-date=9 November 2023 |title=GRAPHENITE – GRAPHENE INFUSED 3D PRINTER POWDER – 30 Lbs – $499.95 |publisher=Noble3DPrinters |work=noble3dprinters.com |access-date=16 July 2015 }}</ref> Many other uses for graphene have been proposed or are under development, in areas including electronics, [[biological engineering]], [[filtration]], lightweight/strong [[composite materials]], [[photovoltaic]]s and [[energy storage]].<ref name="auto"/><ref>{{cite web |url=http://www.graphenea.com/pages/graphene-uses-applications |title=Graphene Uses & Applications |publisher=Graphenea |access-date=13 April 2014 |archive-date=11 February 2014 |archive-url=https://web.archive.org/web/20140211025208/http://www.graphenea.com/pages/graphene-uses-applications |url-status=live }}</ref> Graphene is often produced as a powder and as a dispersion in a polymer matrix. This dispersion is supposedly suitable for advanced composites,<ref>{{cite journal |pmid=23405887 |pmc=3601907 |year=2013 |last1=Lalwani |first1=G |title=Two-dimensional nanostructure-reinforced biodegradable polymeric nanocomposites for bone tissue engineering |journal=Biomacromolecules |volume=14 |issue=3 |pages=900–9 |last2=Henslee |first2=A. M. |last3=Farshid |first3=B |last4=Lin |first4=L |last5=Kasper |first5=F. K. |last6=Qin |first6=Y. X. |last7=Mikos |first7=A. G. |last8=Sitharaman |first8=B |doi=10.1021/bm301995s}}</ref><ref>{{cite journal |first1=M.A. |last1=Rafiee |first2=J. |last2=Rafiee |first3=Z. |last3=Wang |first4=H. |last4=Song |first5=Z.Z. |last5=Yu |first6=N. |last6=Koratkar |s2cid=18266151 |title=Enhanced mechanical properties of nanocomposites at low graphene content |journal=ACS Nano |volume=3 |issue=12 |year=2009 |pages=3884–3890 |doi=10.1021/nn9010472|pmid=19957928 }}</ref> paints and coatings, lubricants, oils and functional fluids, capacitors and batteries, thermal management applications, display materials and packaging, solar cells, inks and 3D-printer materials, and barriers and films.<ref>{{cite web |url=http://www.appliedgraphenematerials.com/products/graphene-dispersions/ |title=Applied Graphene Materials plc :: Graphene dispersions |work=appliedgraphenematerials.com |access-date=26 May 2014 |archive-date=27 May 2014 |archive-url=https://web.archive.org/web/20140527212601/http://www.appliedgraphenematerials.com/products/graphene-dispersions/ |url-status=dead }}</ref>

On August 2, 2016, [[Briggs Automotive Company|Briggs Automative Company's]] new Mono model is said to be made out of graphene as the first of both a street-legal track car and a production car.<ref>{{Cite web |url=http://blog.dupontregistry.com/news/bac-debuts-first-ever-graphene-constructed-vehicle/ |title=BAC Debuts First Ever Graphene Constructed Vehicle |date=2016-08-02 |access-date=2016-08-04 |archive-date=4 August 2016 |archive-url=https://web.archive.org/web/20160804224120/http://blog.dupontregistry.com/news/bac-debuts-first-ever-graphene-constructed-vehicle/ |url-status=live }}</ref>

In January 2018, graphene-based spiral [[inductor]]s exploiting [[kinetic inductance]] at room temperature were first demonstrated at the [[University of California, Santa Barbara]], led by [[Kaustav Banerjee]]. These inductors were predicted to allow significant miniaturization in [[Radio frequency|radio-frequency]] [[integrated circuit]] applications.<ref>{{Cite journal| doi=10.1038/s41928-017-0010-z| title=On-chip intercalated-graphene inductors for next-generation radio frequency electronics| year=2018| last1=Kang| first1=Jiahao| last2=Matsumoto| first2=Yuji| last3=Li| first3=Xiang| last4=Jiang| first4=Junkai| last5=Xie| first5=Xuejun| last6=Kawamoto| first6=Keisuke| last7=Kenmoku| first7=Munehiro| last8=Chu| first8=Jae Hwan| last9=Liu| first9=Wei| last10=Mao| first10=Junfa| last11=Ueno| first11=Kazuyoshi| last12=Banerjee| first12=Kaustav| author12-link=Kaustav Banerjee| journal=Nature Electronics| volume=1| pages=46–51| s2cid=139420526| url=https://escholarship.org/uc/item/2fb2f7h1| access-date=25 August 2020| archive-date=8 June 2020| archive-url=https://web.archive.org/web/20200608230020/https://escholarship.org/uc/item/2fb2f7h1| url-status=live}}</ref><ref>{{Cite web|url=https://www.forbes.com/sites/startswithabang/2018/03/08/breakthrough-in-miniaturized-inductors-to-revolutionize-electronics/#55414a40779e|title=The Last Barrier to Ultra-Miniaturized Electronics is Broken, Thanks To A New Type Of Inductor|last=Siegel|first=E.|year=2018|website=Forbes.com|access-date=8 April 2020|archive-date=1 August 2020|archive-url=https://web.archive.org/web/20200801040010/https://www.forbes.com/sites/startswithabang/2018/03/08/breakthrough-in-miniaturized-inductors-to-revolutionize-electronics/#55414a40779e|url-status=live}}</ref><ref>{{Cite web|url=https://physicsworld.com/a/engineers-reinvent-the-inductor-after-two-centuries/|title=Engineers reinvent the inductor after two centuries|year=2018|website=physicsworld|access-date=8 April 2020|archive-date=8 April 2020|archive-url=https://web.archive.org/web/20200408043458/https://physicsworld.com/a/engineers-reinvent-the-inductor-after-two-centuries/|url-status=live}}</ref>

The potential of epitaxial graphene on [[SiC]] for [[metrology]] has been shown since 2010, displaying quantum Hall resistance quantization accuracy of three parts per billion in monolayer epitaxial graphene. Over the years precisions of parts-per-trillion in the Hall resistance quantization and giant quantum Hall plateaus have been demonstrated. Developments in the encapsulation and doping of epitaxial graphene have led to the commercialization of epitaxial graphene quantum resistance standards.<ref>{{cite journal |last1=Reiss |first1=T. |last2=Hjelt |first2=K. |last3=Ferrari |first3=A.C. |title=Graphene is on track to deliver on its promises |journal=Nature Nanotechnology |date=2019 |volume=14 |issue=907 |pages=907–910 |doi=10.1038/s41565-019-0557-0|pmid=31582830 |bibcode=2019NatNa..14..907R |s2cid=203653976 }}</ref>

Novel uses for graphene continue to be researched and explored. One such use is in combination with water-based epoxy resins to produce anticorrosive coatings.<ref>{{Cite journal |last1=Monetta |first1=T. |last2=Acquesta |first2=A. |last3=Carangelo |first3=A. |last4=Bellucci |first4=F. |date=2018-09-01 |title=Considering the effect of graphene loading in water-based epoxy coatings |url=https://doi.org/10.1007/s11998-018-0045-8 |journal=Journal of Coatings Technology and Research |language=en |volume=15 |issue=5 |pages=923–931 |doi=10.1007/s11998-018-0045-8 |s2cid=139956928 |issn=1935-3804}}</ref> The van der Waals nature of graphene and other two-dimensional (2D) materials also permits van der Waals heterostructures<ref>{{Cite journal |last1=Castellanos-Gomez |first1=Andres |last2=Duan |first2=Xiangfeng |last3=Fei |first3=Zhe |last4=Gutierrez |first4=Humberto Rodriguez |last5=Huang |first5=Yuan |last6=Huang |first6=Xinyu |last7=Quereda |first7=Jorge |last8=Qian |first8=Qi |last9=Sutter |first9=Eli |last10=Sutter |first10=Peter |date=2022-07-28 |title=Van der Waals heterostructures |url=https://www.nature.com/articles/s43586-022-00139-1 |journal=Nature Reviews Methods Primers |language=en |volume=2 |issue=1 |pages=1–19 |doi=10.1038/s43586-022-00139-1 |osti=1891442 |s2cid=251175507 |issn=2662-8449 |access-date=21 April 2023 |archive-date=21 April 2023 |archive-url=https://web.archive.org/web/20230421224309/https://www.nature.com/articles/s43586-022-00139-1 |url-status=live }}</ref> and integrated circuits based on [[Van der Waals integration]] of 2D materials.<ref>{{Cite journal |last1=Meng |first1=Yuan |last2=Feng |first2=Jiangang |last3=Han |first3=Sangmoon |last4=Xu |first4=Zhihao |last5=Mao |first5=Wenbo |last6=Zhang |first6=Tan |last7=Kim |first7=Justin S. |last8=Roh |first8=Ilpyo |last9=Zhao |first9=Yepin |last10=Kim |first10=Dong-Hwan |last11=Yang |first11=Yang |last12=Lee |first12=Jin-Wook |last13=Yang |first13=Lan |last14=Qiu |first14=Cheng-Wei |last15=Bae |first15=Sang-Hoon |date=2023-04-21 |title=Photonic van der Waals integration from 2D materials to 3D nanomembranes |url=https://www.nature.com/articles/s41578-023-00558-w |journal=Nature Reviews Materials |volume=8 |issue=8 |language=en |pages=498–517 |doi=10.1038/s41578-023-00558-w |bibcode=2023NatRM...8..498M |s2cid=258279195 |issn=2058-8437 |access-date=21 April 2023 |archive-date=21 April 2023 |archive-url=https://web.archive.org/web/20230421223403/https://www.nature.com/articles/s41578-023-00558-w |url-status=live }}</ref><ref>{{Cite journal |last1=Liu |first1=Yuan |last2=Huang |first2=Yu |last3=Duan |first3=Xiangfeng |date=March 2019 |title=Van der Waals integration before and beyond two-dimensional materials |journal=Nature |language=en |volume=567 |issue=7748 |pages=323–333 |doi=10.1038/s41586-019-1013-x |pmid=30894723 |bibcode=2019Natur.567..323L |s2cid=256768556 |issn=1476-4687|doi-access=free }}</ref>

Graphene is utilized in detecting gasses and chemicals in environmental monitoring, developing highly sensitive biosensors for medical diagnostics, and creating flexible, wearable sensors for health monitoring.<ref>{{cite book |last1=Shahdeo |first1=Deepshikha |last2=Roberts |first2=Akanksha |year=2020 |title=Comprehensive Analytical Chemistry |chapter=Graphene based sensors |editor=Chaudhery Mustansar Hussain |volume=91 |pages=175–199 |doi=10.1016/bs.coac.2020.08.007 |doi-access=free|isbn=978-0-323-85371-2 }}</ref><ref>{{cite journal |last1=Liu |first1=Jihong |last2=Bao |first2=Siyu |year=2022 |title=Applications of Graphene-Based Materials in Sensors: A Review |journal=Micromachines |volume=13 |issue=2 |page=184 |doi=10.3390/mi13020184 |doi-access=free |pmc=8880160 |pmid=35208308}}</ref> Graphene's transparency also enhances optical sensors, making them more effective in imaging and spectroscopy.<ref>{{cite journal |last1=Li |first1=Zongwen |last2=Zhang |first2=Wenfei |year=2019 |title=Graphene Optical Biosensors |journal=Int J Mol Sci |volume=20 |issue=10 |page=2461 |doi=10.3390/ijms20102461 |doi-access=free |pmc=6567174 |pmid=31109057}}</ref>

== Toxicity ==

One review on graphene toxicity published in 2016 by Lalwani et al. summarizes the [[in vitro]], [[in vivo]], antimicrobial and environmental effects and highlights the various mechanisms of graphene toxicity.<ref name=lalwani16>{{cite journal |pmid=27154267 |pmc=5039077 |year=2016 |last1=Lalwani |first1=Gaurav |title=Toxicology of graphene-based nanomaterials |journal=Advanced Drug Delivery Reviews |volume=105 |issue=Pt B |pages=109–144 |last2=D'Agati |first2=Michael |last3=Mahmud Khan |first3=Amit |last4=Sitharaman |first4=Balaji |doi=10.1016/j.addr.2016.04.028 }}</ref> Another review published in 2016 by Ou et al. focused on graphene-family nanomaterials (GFNs) and revealed several typical mechanisms such as physical destruction, [[oxidative stress]], [[DNA]] damage, inflammatory response, [[apoptosis]], [[autophagy]], and [[necrosis]].<ref name="ou16">{{cite journal |doi=10.1186/s12989-016-0168-y|pmc=5088662| title = Toxicity of graphene-family nanoparticles: A general review of the origins and mechanisms | year = 2016 | last1 = Ou | first1 = Lingling | last2 = Song | first2 = Bin | last3 = Liang | first3 = Huimin | last4 = Liu | first4 = Jia | last5 = Feng | first5=Xiaoli|last6=Deng|first6=Bin|last7=Sun|first7=Ting|last8=Shao|first8=Longquan|journal=Particle and Fibre Toxicology|volume=13|issue=1|page=57|pmid=27799056 |doi-access=free |bibcode=2016PFTox..13...57O }}</ref>

A 2020 study showed that the toxicity of graphene is dependent on several factors such as shape, size, purity, post-production processing steps, oxidative state, functional groups, dispersion state, synthesis methods, route and dose of administration, and exposure times.<ref>{{cite journal|pmc=7287048|year=2020|last1=Joshi |first1= Shubhi |title=Green synthesis of peptide-functionalized reduced graphene oxide (rGO) nano bioconjugate with enhanced antibacterial activity|journal= Scientific Reports |volume=10 |issue=9441|last2=Siddiqui |first2=Ruby |last3=Sharma |first3=Pratibha |last4=Kumar |first4=Rajesh |last5=Verma |first5=Gaurav |last6=Saini |first6=Avneet|page=9441|doi=10.1038/s41598-020-66230-3 |pmid=32523022|bibcode=2020NatSR..10.9441J}}</ref>

In 2014, research at [[Stony Brook University]] showed that [[graphene nanoribbon]]s, graphene nanoplatelets, and graphene nano–onions are non-toxic at concentrations up to 50&nbsp;μg/ml. These nanoparticles do not alter the differentiation of human bone marrow [[Stem cell|stem cells]] towards [[Osteoblast|osteoblasts]] (bone) or [[Adipocyte|adipocytes]] (fat), suggesting that at low doses, graphene nanoparticles are safe for biomedical applications.<ref>{{cite journal |pmid=24674462 |pmc=3995421 |year=2014 |last1=Talukdar |first1=Y |title=The effects of graphene nanostructures on mesenchymal stem cells |journal=Biomaterials |volume=35 |issue=18 |pages=4863–77 |last2=Rashkow |first2=J. T. |last3=Lalwani |first3=G |last4=Kanakia |first4=S |last5=Sitharaman |first5=B |doi=10.1016/j.biomaterials.2014.02.054 }}</ref> In 2013, research at [[Brown University]] found that 10 μm few-layered graphene flakes can pierce [[Cell membrane|cell membranes]] in solution. They were observed to enter initially via sharp and jagged points, allowing graphene to be internalized in the cell. The physiological effects of this remain unknown, and this remains a relatively unexplored field.<ref name=brownedu>{{cite web |first=Kevin |last=Stacey |date=10 July 2013 |url=https://news.brown.edu/articles/2013/07/graphene |title=Jagged graphene edges can slice and dice cell membranes - News from Brown |work=brown.edu |access-date=9 March 2015 |archive-date=25 March 2015 |archive-url=https://web.archive.org/web/20150325093234/https://news.brown.edu/articles/2013/07/graphene |url-status=live }}</ref><ref name=li13>{{Cite journal |doi=10.1073/pnas.1222276110 |pmid=23840061 |pmc=3725082 |title=Graphene microsheets enter cells through spontaneous membrane penetration at edge asperities and corner sites |journal=Proceedings of the National Academy of Sciences |volume=110 |issue=30 |pages=12295–12300 |year=2013 |last1=Li |first1=Y. |last2=Yuan |first2=H. |last3=von Dem Bussche |first3=A. |last4=Creighton |first4=M. |last5=Hurt |first5=R. H. |last6=Kane |first6=A. B. |last7=Gao |first7=H. |bibcode=2013PNAS..11012295L|doi-access=free }}</ref>

== See also ==
* {{annotated link|Borophene}}
* {{annotated link|Carbon fiber}}
* {{annotated link|Penta-graphene}}
* {{annotated link|Phagraphene}}
* {{annotated link|Plumbene}}
* {{annotated link|Silicene}}

==References==

<references>
<ref name="camdic">{{cite web |title=graphene definition, meaning – what is graphene in the British English Dictionary & Thesaurus – Cambridge Dictionaries Online |url=http://dictionary.cambridge.org/dictionary/british/graphene |url-status=live |archive-url=https://web.archive.org/web/20150717152916/http://dictionary.cambridge.org/dictionary/british/graphene |archive-date=17 July 2015 |access-date=4 October 2024 |work=cambridge.org}}</ref>
<ref name="brod1859">{{cite journal |last=Brodie |first=B. C. |year=1859 |title=On the Atomic Weight of Graphite |journal=[[Philosophical Transactions of the Royal Society of London]] |volume=149 |pages=249–259 |bibcode=1859RSPT..149..249B |jstor=108699 |doi=10.1098/rstl.1859.0013|doi-access=free }}</ref>
<ref name="deb1916">{{cite journal |year=1916 |title=Interferenz an regellos orientierten Teilchen im Röntgenlicht I |journal=Physikalische Zeitschrift |language=de |volume=17 |page=277 |url=http://resolver.sub.uni-goettingen.de/purl?PPN252457811_1916/dmdlog4 |last1=Debije |first1=P |last2=Scherrer |first2=P |author-link1=Peter Debye |access-date=13 April 2014 |archive-date=14 April 2014 |archive-url=https://web.archive.org/web/20140414151901/http://resolver.sub.uni-goettingen.de/purl?PPN252457811_1916/dmdlog4 |url-status=live }}</ref>
<ref name="deb1917">{{cite journal |year=1917 |title=Über die Konstitution von Graphit und amorpher Kohle |trans-title=On the Structure of Graphite and Amorphous Carbon |journal=Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse |language=de |volume=1917 |page=180-188 |last1=Debye |first1=Peter |last2=Scherrer |first2=Paul |author-link1=Peter Debye |author-link2=Paul Scherrer |url=https://eudml.org/doc/58985}}</ref>
<ref name="hull1917">{{cite journal |year=1917 |title=A New Method of X-ray Crystal Analysis |journal=Phys. Rev. |language=en |volume=10 |issue=6 |page=661-696 |last=Hull |first=AW |author-link=Albert Hull |doi=10.1103/PhysRev.10.661|bibcode=1917PhRv...10..661H }}</ref>
<ref name="kohl1918">{{cite journal |last1=Kohlschütter |first1=V. |last2=Haenni |first2=P. |year=1919 |title=Zur Kenntnis des Graphitischen Kohlenstoffs und der Graphitsäure |trans-title=To the knowledge of graphitic carbon and graphitic acid |language=de |journal=[[Zeitschrift für anorganische und allgemeine Chemie]] |volume=105 |issue=1 |pages=121–144 |doi=10.1002/zaac.19191050109 |url=https://zenodo.org/record/1428166 |access-date=12 April 2020 |archive-date=1 August 2020 |archive-url=https://web.archive.org/web/20200801035845/https://zenodo.org/record/1428166 |url-status=live }}</ref>
<ref name="bern1924">{{cite journal |last=Bernal |first=JD |author-link=John Desmond Bernal |year=1924 |title=The Structure of Graphite |jstor=94336 |journal=Proc. R. Soc. Lond. |volume=A106 |issue=740 |pages=749–773 |doi=10.1098/rspa.1924.0101 |bibcode=1924RSPSA.106..749B|doi-access=free }}</ref>
<ref name="tru1975">{{cite journal |last1=Trucano |first1=Peter |last2=Chen |first2=Ruey |title=Structure of graphite by neutron diffraction |journal=Nature |volume=258 |issue=5531 |pages=136–137 |date=13 November 1975 |doi=10.1038/258136a0|bibcode=1975Natur.258..136T }}</ref>
<ref name="howe2003">{{cite journal |last1=Howe |first1=JY |last2=Rawn |first2=CJ |last3=Jones |first3=LE |last4=Ow |first4=H |title=Improved crystallographic data for graphite |journal=Powder Diffraction |volume=18 |issue=2 |pages=150–154 |date=June 2003 |doi=10.1154/1.1536926|bibcode=2003PDiff..18..150H }}</ref>
<ref name="ruess1948">{{cite journal |last1=Ruess |first1=G. |last2=Vogt |first2=F. |year=1948 |title=Höchstlamellarer Kohlenstoff aus Graphitoxyhydroxyd |language=de |journal=[[Monatshefte für Chemie]] |volume=78 |issue=3–4 |pages=222–242 |doi=10.1007/BF01141527}}</ref>
<ref name="boehm1962b">{{cite book |chapter-url=http://www.americancarbonsociety.org/sites/default/files/conference/1961/1961_V1_73.PDF |title=Proceedings of the Fifth Conference on Carbon |last1=Boehm |first1=H. P. |last2=Clauss |first2=A. |last3=Fischer |first3=G. |last4=Hofmann |first4=U. |publisher=[[Pergamon Press]] |year=1962 |chapter=Surface Properties of Extremely Thin Graphite Lamellae |access-date=1 April 2016 |archive-date=13 April 2016 |archive-url=https://web.archive.org/web/20160413102339/http://www.americancarbonsociety.org/sites/default/files/conference/1961/1961_V1_73.PDF |url-status=dead }}</ref>
<ref name="divi1984">{{cite journal |last1=DiVincenzo |first1=D. P. |last2=Mele |first2=E. J. |title=Self-Consistent Effective Mass Theory for Intralayer Screening in Graphite Intercalation Compounds |doi=10.1103/PhysRevB.29.1685 |journal=Physical Review B |volume=295 |pages=1685–1694 |year=1984 |bibcode=1984PhRvB..29.1685D |issue=4}}</ref>
<ref name="mour1987">{{cite journal |last=Mouras |first=S. |title=Synthesis of first stage graphite intercalation compounds with fluorides |journal=Revue de Chimie Minérale |id={{INIST|7578318}} |volume=24 |page=572 |year=1987 |issue=1 |doi=10.1016/0022-1139(87)95120-7 |bibcode=1987JFluC..35..151H |display-authors=etal}}</ref>
<ref name="saito1992">{{cite journal |last1=Saito |first1=R. |last2=Fujita |first2=Mitsutaka |last3=Dresselhaus |first3=G. |last4=Dresselhaus |first4=M. |author-link4=Mildred Dresselhaus|title=Electronic structure of graphene tubules based on C60 |doi=10.1103/PhysRevB.46.1804 |pmid=10003828 |journal=Physical Review B |volume=46 |pages=1804–1811 |year=1992 |bibcode=1992PhRvB..46.1804S |issue=3}}</ref>
<ref name="bern1996">{{cite journal |author=Bernatowicz |author2=T. J. <!-- check this --> |last3=Gibbons |first3=Patrick C. |last4=Lodders |first4=Katharina |last5=Fegley |first5=Bruce |last6=Amari |first6=Sachiko |last7=Lewis |first7=Roy S. |display-authors=2 |year=1996 |title=Constraints on stellar grain formation from presolar graphite in the Murchison meteorite |journal=Astrophysical Journal |volume=472 |pages=760–782 |doi=10.1086/178105 |bibcode=1996ApJ...472..760B |issue=2|doi-access=free }}</ref>
<ref name="oshi1997">{{cite journal |last1=Oshima |first1=C. |last2=Nagashima |first2=A. |title=Ultra-thin epitaxial films of graphite and hexagonal boron nitride on solid surfaces |doi=10.1088/0953-8984/9/1/004 |journal=J. Phys.: Condens. Matter |volume=9 |issue=1 |pages=1–20 |year=1997 |bibcode=1997JPCM....9....1O|s2cid=250758301 }}</ref>
<ref name="forb1998">{{cite journal |last1=Forbeaux |first1=I. |last2=Themlin |first2=J.-M. |last3=Debever |first3=J.-M. |title=Heteroepitaxial graphite on 6H-SiC(0001): Interface formation through conduction-band electronic structure |doi=10.1103/PhysRevB.58.16396 |journal=Physical Review B |volume=58 |pages=16396–16406 |year=1998 |bibcode=1998PhRvB..5816396F |issue=24}}</ref>
<ref name="wang2000">{{cite journal |last1=Wang |first1=S. |last2=Yata |first2=S. |last3=Nagano |first3=J. |last4=Okano |first4=Y. |last5=Kinoshita |first5=H. |last6=Kikuta |first6=H. |last7=Yamabe |first7=T. |title=A new carbonaceous material with large capacity and high efficiency for rechargeable Li-ion batteries |doi=10.1149/1.1393559 |journal=Journal of the Electrochemical Society |volume=147 |page=2498 |year=2000 |issue=7|bibcode=2000JElS..147.2498W }}</ref>
<ref name="fraun2002">{{cite journal |last1=Fraundorf |first1=P. |last2=Wackenhut |first2=M. |year=2002 |title=The core structure of presolar graphite onions |journal=Astrophysical Journal Letters |volume=578 |page=L153–156 |arxiv=astro-ph/0110585 |doi=10.1086/344633 |bibcode=2002ApJ...578L.153F |issue=2|s2cid=15066112 }}</ref>
<ref name="jang2002">Bor Z. Jang and Wen C. Huang (2002): "[https://patentimages.storage.googleapis.com/e5/3d/0d/1c25e5f68a77ab/US7071258.pdf Nano-scaled graphene plates] {{Webarchive|url=https://web.archive.org/web/20201022100950/https://patentimages.storage.googleapis.com/e5/3d/0d/1c25e5f68a77ab/US7071258.pdf |date=22 October 2020 }}".  US Patent 7071258. Filed on 2002-10-21, granted on 2006-07-04, assigned to Global Graphene Group Inc; to expire on 2024-01-06.</ref>
<ref name="kasu2002">{{cite journal |last1=Kasuya |first1=D. |last2=Yudasaka |first2=M. |last3=Takahashi |first3=K. |last4=Kokai |first4=F. |last5=Iijima |first5=S. |title=Selective Production of Single-Wall Carbon Nanohorn Aggregates and Their Formation Mechanism |doi=10.1021/jp020387n |journal=J. Phys. Chem. B |volume=106 |year=2002 |pages=4947–4951 |issue=19}}</ref>
<ref name="ruth2002">Robert B. Rutherford and Richard L. Dudman (2002): "[https://patentimages.storage.googleapis.com/d3/9c/39/d4ef201b0e4727/US6667100.pdf Ultra-thin flexible expanded graphite heating element] {{Webarchive|url=https://web.archive.org/web/20201022094622/https://patentimages.storage.googleapis.com/d3/9c/39/d4ef201b0e4727/US6667100.pdf |date=22 October 2020 }}". US Patent 6667100. Filed on 2002-05-13, granted on 2003-12-23, assigned to  EGC Operating Co LLC; expired.</ref>
<ref name="kope2003">{{cite journal |last1=Kopelevich |first1=Y. |last2=Torres |first2=J. |last3=Da Silva |first3=R. |last4=Mrowka |first4=F. |last5=Kempa |first5=H. |last6=Esquinazi |first6=P. |title=Reentrant Metallic Behavior of Graphite in the Quantum Limit |journal=Physical Review Letters |year=2003 |volume=90 |page=156402 |doi=10.1103/PhysRevLett.90.156402 |issue=15 |pmid=12732058 |arxiv=cond-mat/0209406 |bibcode=2003PhRvL..90o6402K|s2cid=26968734 }}</ref>
<ref name="luky2004">{{cite journal |first1=Igor A. |last1=Luk'yanchuk |first2=Yakov |last2=Kopelevich |title=Phase Analysis of Quantum Oscillations in Graphite |journal=Physical Review Letters |year=2004 |volume=93 |page=166402 |doi=10.1103/PhysRevLett.93.166402 |issue=16 |pmid=15525015 |arxiv=cond-mat/0402058 |bibcode=2004PhRvL..93p6402L|s2cid=17130602 }}</ref>
<ref name="novo2004">{{cite journal |last1=Novoselov |first1=K. S. |last2=Geim |first2=AK |last3=Morozov |first3=SV |last4=Jiang |first4=D |last5=Zhang |first5=Y |last6=Dubonos |first6=SV |last7=Grigorieva |first7=IV |last8=Firsov |first8=AA |title=Electric Field Effect in Atomically Thin Carbon Films |journal=Science |date=22 October 2004 |volume=306 |issue=5696 |pages=666–669 |doi=10.1126/science.1102896 |pmid=15499015 |arxiv=cond-mat/0410550 |bibcode=2004Sci...306..666N |s2cid=5729649 }}</ref>
<ref name="gusy2005">{{cite journal |last1=Gusynin |first1=V. P. |last2=Sharapov |first2=S. G. |title=Unconventional Integer Quantum Hall Effect in Graphene |doi=10.1103/PhysRevLett.95.146801 |journal=Physical Review Letters |volume=95 |page=146801 |year=2005 |pmid=16241680 |bibcode=2005PhRvL..95n6801G |arxiv=cond-mat/0506575 |issue=14|s2cid=37267733 }}</ref>
<ref name="novo2005">{{cite journal |last1=Novoselov |first1=K. S. |last2=Geim |first2=A. K. |last3=Morozov |first3=S. V. |last4=Jiang |first4=D. |last5=Katsnelson |first5=M. I. |last6=Grigorieva |first6=I. V. |last7=Dubonos |first7=S. V. |last8=Firsov |first8=A. A. |title=Two-dimensional gas of massless Dirac fermions in graphene |doi=10.1038/nature04233 |journal=Nature |volume=438 |pages=197–200 |year=2005 |pmid=16281030 |issue=7065 |arxiv=cond-mat/0509330 |bibcode=2005Natur.438..197N|s2cid=3470761 }}</ref>
<ref name="zhang2005">{{cite journal |last1=Zhang |first1=Y. |last2=Tan |first2=Y. W. |last3=Stormer |first3=H. L. |last4=Kim |first4=P. |title=Experimental observation of the quantum Hall effect and Berry's phase in graphene |doi=10.1038/nature04235 |journal=Nature |volume=438 |pages=201–204 |year=2005 |pmid=16281031 |issue=7065 |arxiv=cond-mat/0509355 |bibcode=2005Natur.438..201Z|s2cid=4424714 }}</ref>
<ref name="shen2006">{{cite journal |last1=Shenderova |first1=O. A. |last2=Zhirnov |first2=V. V. |last3=Brenner |first3=D. W. |title=Carbon Nanostructures |journal=Critical Reviews in Solid State and Materials Sciences |date=July 2002 |volume=27 |issue=3–4 |pages=227–356 |doi=10.1080/10408430208500497 |bibcode=2002CRSSM..27..227S |s2cid=214615777 }}</ref>
<ref name="carl2007">{{cite journal |last=Carlsson |first=J. M. |title=Graphene: Buckle or break |doi=10.1038/nmat2051 |journal=Nature Materials |volume=6 |year=2007 |pmid=17972931 |issue=11 |bibcode=2007NatMa...6..801C |pages=801–2|hdl=11858/00-001M-0000-0010-FF61-1 |hdl-access=free }}</ref>
<ref name="faso2007">{{cite journal |last1=Fasolino |first1=A. |last2=Los |first2=J. H. |last3=Katsnelson |first3=M. I. |title=Intrinsic ripples in graphene |doi=10.1038/nmat2011 |journal=Nature Materials |volume=6 |year=2007 |pmid=17891144 |issue=11 |bibcode=2007NatMa...6..858F |pages=858–61 |arxiv=0704.1793|s2cid=38264967 }}</ref>
<ref name="geim2007">{{cite journal |last1=Geim |first1=A. K. |author-link=Andre Geim |last2=Novoselov |first2=K. S. |author-link2=Konstantin Novoselov |date=2007-02-26 |title=The rise of graphene |journal=[[Nature Materials]] |volume=6 |issue=3 |pages=183–191 |arxiv=cond-mat/0702595 |bibcode=2007NatMa...6..183G |doi=10.1038/nmat1849 |pmid=17330084 |s2cid=14647602}}</ref>
<ref name="ishi2007">{{cite journal |last=Ishigami |first=Masa |year=2007 |volume=7 |issue=6 |pages=1643–1648 |title=Atomic Structure of Graphene on SiO<sub>2</sub> |journal=Nano Letters |doi=10.1021/nl070613a |pmid=17497819 |bibcode=2007NanoL...7.1643I |display-authors=etal|arxiv=0811.0587 |s2cid=13087073 }}</ref>
<ref name="meyer2007">{{cite journal |last1=Meyer |first1=J. |last2=Geim |first2=A. K. |last3=Katsnelson |first3=M. I. |last4=Novoselov |first4=K. S. |last5=Booth |first5=T. J. |last6=Roth |first6=S. |title=The structure of suspended graphene sheets |journal=Nature |volume=446 |pages=60–63 |year=2007 |doi=10.1038/nature05545 |pmid=17330039 |issue=7131 |arxiv=cond-mat/0701379 |bibcode=2007Natur.446...60M|s2cid=3507167 }}</ref>
<ref name="geim2008">{{cite news |last1=Geim |first1=A. K. |last2=Kim |first2=P. |date=April 2008 |title=Carbon Wonderland |url=http://www.scientificamerican.com/article.cfm?id=carbon-wonderland |work=[[Scientific American]] |quote="... bits of graphene are undoubtedly present in every pencil mark"}}</ref>
<ref name="lee2008">{{cite journal|last=Lee|first=Changgu|date=2008|title=Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene|journal=Science|volume=321|issue=385|pages=385–388|bibcode=2008Sci...321..385L|doi=10.1126/science.1157996|pmid=18635798|s2cid=206512830}}</ref>
<ref name="nair2008">{{cite journal |last1=Nair |first1=R. R. |last2=Blake |first2=P. |last3=Grigorenko |first3=A. N. |last4=Novoselov |first4=K. S. |last5=Booth |first5=T. J. |last6=Stauber |first6=T. |last7=Peres |first7=N. M. R. |last8=Geim |first8=A. K. |title=Fine Structure Constant Defines Visual Transparency of Graphene |journal=Science |date=6 June 2008 |volume=320 |issue=5881 |pages=1308 |doi=10.1126/science.1156965 |pmid=18388259 |bibcode=2008Sci...320.1308N|arxiv=0803.3718 |s2cid=3024573 }}</ref>
<ref name="IUPAC2009">{{cite book |chapter=graphene layer |chapter-url=http://goldbook.iupac.org/G02683.html |publisher=International Union of Pure and Applied Chemistry |access-date=31 March 2012|doi=10.1351/goldbook.G02683 |title=IUPAC Compendium of Chemical Terminology |year=2009 |isbn=978-0-9678550-9-7 }}</ref>
<ref name="aps2009">{{cite journal |year=2009 |url=http://www.aps.org/publications/apsnews/200910/loader.cfm?csModule=security/getfile&pageid=187967 |title=This Month in Physics History: October 22, 2004: Discovery of Graphene |page=2 |series=Series II |volume=18 |issue=9 |journal=[[APS News]] |access-date=6 October 2013 |archive-date=3 July 2020 |archive-url=https://web.archive.org/web/20200703130616/https://www.aps.org/publications/apsnews/200910/loader.cfm?csModule=security/getfile&pageid=187967 |url-status=dead }}</ref>
<ref name="bao2009">{{cite journal |last1=Bao |first1=Qiaoliang |last2=Zhang |first2=Han |last3=Wang |first3=Yu |last4=Ni |first4=Zhenhua |last5=Yan |first5=Yongli |last6=Shen |first6=Ze Xiang |last7=Loh |first7=Kian Ping |last8=Tang |first8=Ding Yuan |title=Atomic-Layer Graphene as a Saturable Absorber for Ultrafast Pulsed Lasers |journal=Advanced Functional Materials |date=9 October 2009 |volume=19 |issue=19 |pages=3077–3083 |doi=10.1002/adfm.200901007 |bibcode=2009arXiv0910.5820B |arxiv=0910.5820 |s2cid=59070301 }}</ref>
<ref name="grtim2009">{{cite web |url=http://graphenetimes.com/2009/12/boehms-1961-isolation-of-graphene/ |title=Boehm's 1961 isolation of graphene |work=Graphene Times |date=7 December 2009 |url-status=dead |archive-url=https://web.archive.org/web/20101008144828/http://graphenetimes.com/2009/12/boehms-1961-isolation-of-graphene/ |archive-date=8 October 2010}}</ref>
<ref name="peres2009">{{cite journal |last1=Peres |first1=N. M. R. |last2=Ribeiro |first2=R. M. |year=2009 |title=Focus on Graphene |journal=[[New Journal of Physics]] |volume=11 |issue=9 |page=095002 |bibcode=2009NJPh...11i5002P |doi=10.1088/1367-2630/11/9/095002 |doi-access=free}}</ref>
<ref name="ried2009">{{cite journal |last1=Riedl |first1=C. |last2=Coletti |first2=C. |last3=Iwasaki |first3=T. |last4=Zakharov |first4=A.A. |last5=Starke |first5=U. |year=2009 |title=Quasi-Free-Standing Epitaxial Graphene on SiC Obtained by Hydrogen Intercalation |journal=Physical Review Letters |volume=103 |page=246804 |doi=10.1103/PhysRevLett.103.246804 |pmid=20366220 |bibcode=2009PhRvL.103x6804R |issue=24 |arxiv=0911.1953|s2cid=33832203 }}</ref>
<ref name="geim2009a">{{cite journal |last=Geim |first=A. |year=2009 |title=Graphene: Status and Prospects |journal=Science |pmid=19541989 |volume=324 |issue=5934 |doi=10.1126/science.1158877 |bibcode=2009Sci...324.1530G |pages=1530–4 |arxiv=0906.3799|s2cid=206513254 }}</ref>
<ref name="zhang2009a">{{cite journal |last1=Zhang |first1=H. |last2=Tang |first2=D. Y. |last3=Zhao |first3=L. M. |last4=Bao |first4=Q. L. |last5=Loh |first5=K. P. |title=Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene |journal=Optics Express |date=28 September 2009 |volume=17 |issue=20 |pages=17630–17635 |doi=10.1364/OE.17.017630 |pmid=19907547 |bibcode=2009OExpr..1717630Z |arxiv=0909.5536 |s2cid=207313024 }}</ref>
<ref name="zhang2009b">{{cite journal |last1=Zhang |first1=Han |last2=Bao |first2=Qiaoliang |last3=Tang |first3=Dingyuan |last4=Zhao |first4=Luming |last5=Loh |first5=Kianping |title=Large energy soliton erbium-doped fiber laser with a graphene-polymer composite mode locker |journal=Applied Physics Letters |date=5 October 2009 |volume=95 |issue=14 |pages=141103 |doi=10.1063/1.3244206 |arxiv=0909.5540 |bibcode=2009ApPhL..95n1103Z |s2cid=119284608 }}</ref>
<ref name="zhang2009c">{{cite journal |last=Zhang |title=Graphene: Mode-locked lasers |journal=NPG Asia Materials |year=2009 |doi=10.1038/asiamat.2009.52|doi-access=free }}</ref>
<ref name="ukiop2010">{{cite web |url=http://physicsworld.com/cws/article/news/43939 |title=Graphene pioneers bag Nobel prize |publisher=[[Institute of Physics]], UK |date=5 October 2010 |access-date=5 October 2010 |archive-date=8 October 2010 |archive-url=https://web.archive.org/web/20101008071254/http://physicsworld.com/cws/article/news/43939 |url-status=dead }}</ref>
<ref name="zhang2010a">{{cite journal |last1=Zhang |first1=Han |last2=Tang |first2=Dingyuan |last3=Knize |first3=R. J. |last4=Zhao |first4=Luming |last5=Bao |first5=Qiaoliang |last6=Loh |first6=Kian Ping |title=Graphene mode locked, wavelength-tunable, dissipative soliton fiber laser |journal=Applied Physics Letters |date=15 March 2010 |volume=96 |issue=11 |pages=111112 |doi=10.1063/1.3367743 |bibcode=2010ApPhL..96k1112Z |arxiv=1003.0154 |s2cid=119233725 }}</ref>
<ref name="kurum2011">{{cite journal |last1=Kurum |first1=U. |last2=Liu |first2=Bo |last3=Zhang |first3=Kailiang |last4=Liu |first4=Yan |last5=Zhang |first5=Hao |title=Electrochemically tunable ultrafast optical response of graphene oxide |journal=Applied Physics Letters |volume=98 |page=141103 |year=2011 |bibcode=2011ApPhL..98b1103M |doi=10.1063/1.3540647 |issue=2}}</ref>
<ref name="bolm2011a">{{cite journal |first1=Dima |last1=Bolmatov |first2=Chung-Yu |last2=Mou |title=Graphene-based modulation-doped superlattice structures |journal=Journal of Experimental and Theoretical Physics |volume=112 |issue=1 |pages=102–107 |year=2011 |doi=10.1134/S1063776111010043 |arxiv=1011.2850 |bibcode=2011JETP..112..102B|s2cid=119223424 }}</ref>
<ref name="bolm2011b">{{cite journal |first=Dima |last=Bolmatov |title=Thermodynamic properties of tunneling quasiparticles in graphene-based structures |journal=Physica C |volume=471 |pages=1651–1654 |year=2011 |doi=10.1016/j.physc.2011.07.008 |issue=23–24 |arxiv=1106.6331 |bibcode=2011PhyC..471.1651B|s2cid=118596336 }}</ref>
<ref name="coop2012">{{cite journal |last1=Cooper |first1=Daniel R. |last2=D'Anjou |first2=Benjamin |last3=Ghattamaneni |first3=Nageswara |last4=Harack |first4=Benjamin |last5=Hilke |first5=Michael |last6=Horth |first6=Alexandre |last7=Majlis |first7=Norberto |last8=Massicotte |first8=Mathieu |last9=Vandsburger |first9=Leron |last10=Whiteway |first10=Eric |last11=Yu |first11=Victor |title=Experimental Review of Graphene |journal=ISRN Condensed Matter Physics |date=26 April 2012 |volume=2012 |pages=1–56 |doi=10.5402/2012/501686 |bibcode=2011arXiv1110.6557C |arxiv=1110.6557 |s2cid=78304205 |doi-access=free }}</ref>
<ref name="geim2012">{{cite journal |last=Geim |first=A. K. |year=2012 |title=Graphene Prehistory |journal=[[Physica Scripta]] |volume=T146 |page=014003 |bibcode=2012PhST..146a4003G |doi=10.1088/0031-8949/2012/T146/014003|doi-access=free }}</ref>
<ref name="puiu2012">{{cite journal |last1=Bonaccorso |first1=Francesco |last2=Colombo |first2=Luigi |last3=Yu |first3=Guihua |last4=Stoller |first4=Meryl |last5=Tozzini |first5=Valentina |last6=Ferrari |first6=Andrea C. |last7=Ruoff |first7=Rodney S. |last8=Pellegrini |first8=Vittorio |title=Graphene, related two-dimensional crystals, and hybrid systems for energy conversion and storage |journal=Science |date=2 January 2015 |volume=347 |issue=6217 |pages=1246501 |doi=10.1126/science.1246501 |pmid=25554791 |bibcode=2015Sci...347...41B |s2cid=6655234 }}</ref>
<ref name="denis2013">{{cite journal |last1=Denis |first1=P. A. |last2=Iribarne |first2=F. |title=Comparative Study of Defect Reactivity in Graphene |doi=10.1021/jp4061945 |journal=Journal of Physical Chemistry C |volume=117 |pages=19048–19055 |year=2013 |issue=37}}</ref>
<ref name="Yamada3">{{cite journal |last1=Yamada |first1=Y. |last2=Murota |first2=K |last3=Fujita |first3=R |last4=Kim |first4=J |s2cid=12628957 |title=Subnanometer vacancy defects introduced on graphene by oxygen gas |doi=10.1021/ja4117268 |pmid=24460150 |journal=Journal of the American Chemical Society |volume=136 |issue=6 |pages=2232–2235 |year=2014 |bibcode=2014JAChS.136.2232Y |display-authors=etal}}</ref>
<ref name="Eftekhari">{{cite journal |last1=Eftekhari |first1=A. |last2=Jafarkhani |first2=P. |title=Curly Graphene with Specious Interlayers Displaying Superior Capacity for Hydrogen Storage |doi=10.1021/jp410044v |journal=Journal of Physical Chemistry C |volume=117 |pages=25845–25851 |year=2013 |issue=48}}</ref>
<ref name="Yamada1">{{cite journal |last1=Yamada |first1=Y. |last2=Yasuda |first2=H. |last3=Murota |first3=K. |last4=Nakamura |first4=M. |last5=Sodesawa |first5=T. |last6=Sato |first6=S. |title=Analysis of heat-treated graphite oxide by X-ray photoelectron spectroscopy |doi=10.1007/s10853-013-7630-0 |journal=Journal of Materials Science |volume=48 |pages=8171–8198 |year=2013 |issue=23|bibcode=2013JMatS..48.8171Y |s2cid=96586004 }}</ref>
<ref name="Yamada2">{{cite journal |last1=Yamada |first1=Y. |last2=Kim |first2=J. |last3=Murota |first3=K. |last4=Matsuo |first4=S. |last5=Sato |first5=S. |title=Nitrogen-containing graphene analyzed by X-ray photoelectron spectroscopy |doi=10.1016/j.carbon.2013.12.061 |journal=Carbon |volume=70 |pages=59–74 |year=2014|bibcode=2014Carbo..70...59Y }}</ref>
<ref name="tang2012">{{cite journal |last1=Tang |first1=Libin |last2=Ji |first2=Rongbin |last3=Li |first3=Xueming |last4=Bai |first4=Gongxun |last5=Liu |first5=Chao Ping |last6=Hao |first6=Jianhua |last7=Lin |first7=Jingyu |last8=Jiang |first8=Hongxing |last9=Teng |first9=Kar Seng |last10=Yang |first10=Zhibin |last11=Lau |first11=Shu Ping |title=Deep Ultraviolet to Near-Infrared Emission and Photoresponse in Layered N-Doped Graphene Quantum Dots |journal=ACS Nano |date=2012 |volume=8 |issue=6 |pages=5102–5110 |doi=10.1021/nn501796r|pmid=24848545 |url=https://cronfa.swan.ac.uk/Record/cronfa21239 }}</ref>
<ref name="zan2012">{{cite journal|last1=Zan|first1=Recep|last2=Ramasse|first2=Quentin M.|last3=Bangert|first3=Ursel|author-link3=Ursel Bangert|last4=Novoselov|first4=Konstantin S.|year=2012|title= Graphene Reknits Its Holes|journal= Nano Letters|volume=12|issue=8|pages=3936–3940|arxiv=1207.1487|bibcode=2012NanoL..12.3936Z|doi=10.1021/nl300985q|pmid=22765872|s2cid=11008306}}</ref>
<ref name="zheng2012">{{cite journal |last1=Zheng |first1=Z. |last2=Zhao |first2=Chujun |last3=Lu |first3=Shunbin |last4=Chen |first4=Yu |last5=Li |first5=Ying |last6=Zhang |first6=Han |last7=Wen |first7=Shuangchun |title=Microwave and optical saturable absorption in graphene |journal=Optics Express |year=2012 |volume=20 |issue=21 |pages=23201–23214 |doi=10.1364/OE.20.023201 |pmid=23188285 |bibcode=2012OExpr..2023201Z|doi-access=free }}</ref>
<ref name="felix2013">{{cite journal |last1=Felix |first1=I. M. |title=Estudo da estrutura eletrônica do grafeno e grafeno hidratado |trans-title=Study of the electronic structure of graphene and hydrated graphene |language=pt |url=http://lattes.cnpq.br/8685343970026801 |date=2013}}</ref>
<ref name="lixu2013">{{cite journal |last1=Li |first1=Xueming |last2=Lau |first2=Shu Ping |last3=Tang |first3=Libin |last4=Ji |first4=Rongbin |last5=Yang |first5=Peizhi |s2cid=137213724 |title=Multicolour Light emission from chlorine-doped graphene quantum dots |journal=J. Mater. Chem. C |date=2013 |volume=1 |issue=44 |pages=7308–7313 |doi=10.1039/C3TC31473A|hdl=10397/34810 |hdl-access=free }}</ref>
<ref name="nobel2013">{{cite web |title=The Nobel Prize in Physics 2010 |url=https://www.nobelprize.org/prizes/physics/2010/illustrated-information/#reading |publisher=[[The Nobel Foundation]] |access-date=3 December 2013}}</ref>
<ref name="tang2013">{{cite journal |last1=Tang |first1=Libin |last2=Ji |first2=Rongbin |last3=Li |first3=Xueming |last4=Teng |first4=Kar Seng |last5=Lau |first5=Shu Ping |title=Size-Dependent Structural and Optical Characteristics of Glucose-Derived Graphene Quantum Dots |journal=Particle & Particle Systems Characterization |date=2013 |volume=30 |issue=6 |pages=523–531 |doi=10.1002/ppsc.201200131|hdl=10397/32222 |s2cid=96410135 |hdl-access=free }}</ref>
<ref name="lili2013b">{{cite journal |last1=Li |first1=Lingling |last2=Wu |first2=Gehui |last3=Yang |first3=Guohai |last4=Peng |first4=Juan |last5=Zhao |first5=Jianwei |last6=Zhu |first6=Jun-Jie |s2cid=205874900 |title=Focusing on luminescent graphene quantum dots: current status and future perspectives |journal=Nanoscale |date=2013 |volume=5 |issue=10 |pages=4015–39 |doi=10.1039/C3NR33849E |pmid=23579482 |bibcode=2013Nanos...5.4015L}}</ref>
<ref name="azon2014">{{cite news |title=Global Demand for Graphene after Commercial Production to be Enormous, says Report |publisher=AZONANO.com |url=http://www.azonano.com/news.aspx?newsID=29510 |date=28 February 2014 |access-date=24 July 2014}}</ref>
<ref name="burn2014">{{cite news |first=Rebecca |last=Burn-Callander |title=Graphene maker aims to build British, billion-pound venture |url=http://www.telegraph.co.uk/finance/businessclub/10936423/Graphene-maker-aims-to-build-British-billion-pound-venture.html |archive-url=https://ghostarchive.org/archive/20220111/http://www.telegraph.co.uk/finance/businessclub/10936423/Graphene-maker-aims-to-build-British-billion-pound-venture.html |archive-date=11 January 2022 |url-access=subscription |url-status=live |newspaper=Daily Telegraph |date=1 July 2014 |access-date=24 July 2014}}{{cbignore}}</ref>
<ref name="gibs2014">{{cite news |first=Robert |last=Gibson |title=Consett firm Thomas Swan sees export success with grapheme |publisher=The Journal |url=http://www.thejournal.co.uk/business/business-news/consett-firm-thomas-swan-sees-7243084 |date=10 June 2014 |access-date=23 July 2014 |archive-date=12 July 2014 |archive-url=https://web.archive.org/web/20140712051023/http://www.thejournal.co.uk/business/business-news/consett-firm-thomas-swan-sees-7243084 |url-status=dead }}</ref>
<ref name="grima2014">{{cite journal |last1=Grima |first1=J. N. |last2=Winczewski |first2=S. |last3=Mizzi |first3=L. |last4=Grech |first4=M. C. |last5=Cauchi |first5=R. |last6=Gatt |first6=R. |last7=Attard |first7=D. |last8=Wojciechowski |first8=K.W. |last9=Rybicki |first9=J. |title=Tailoring Graphene to Achieve Negative Poisson's Ratio Properties |doi=10.1002/adma.201404106 |journal=Advanced Materials |year=2014 |volume=27 |issue=8 |pages=1455–1459 |pmid=25504060|s2cid=19738771 }}</ref>
<ref name="lixu2014">{{cite journal |last1=Li |first1=Xueming |last2=Lau |first2=Shu Ping |last3=Tang |first3=Libin |last4=Ji |first4=Rongbin |last5=Yang |first5=Peizhi |s2cid=23688312 |title=Sulphur Doping: A Facile Approach to Tune the Electronic Structure and Optical Properties of Graphene Quantum Dots |journal=Nanoscale |date=2014 |volume=6 |issue=10 |pages=5323–5328 |doi=10.1039/C4NR00693C |pmid=24699893 |bibcode=2014Nanos...6.5323L|hdl=10397/34914 |hdl-access=free }}</ref>
<ref name="manch2014">{{cite web| author=<!--Staff writer(s); no by-line.--> |title=The Story of Graphene |url=http://www.graphene.manchester.ac.uk/explore/the-story-of-graphene|date=10 September 2014 |website=www.graphene.manchester.ac.uk |publisher=The University of Manchester |access-date=9 October 2014 |quote="Following discussions with colleagues, Andre and Kostya adopted a method that researchers in surface science were using – using simple Sellotape to peel away layers of graphite to expose a clean surface for study under the microscope."}}</ref>
<ref name="mrmak2014">{{Cite web|last=Mrmak|first=Nebojsa|date=2014-11-28|title=Graphene properties (A Complete Reference)|url=http://www.graphene-battery.net/graphene-properties.htm|access-date=2019-11-10|website=Graphene-Battery.net}}</ref>
<ref name="tang2014">{{cite journal |last1=Tang |first1=Libin |last2=Ji |first2=Rongbin |last3=Cao |first3=Xiangke |last4=Lin |first4=Jingyu |last5=Jiang |first5=Hongxing |last6=Li |first6=Xueming |last7=Teng |first7=Kar Seng |last8=Luk |first8=Chi Man |last9=Zeng |first9=Songjun |last10=Hao |first10=Jianhua |last11=Lau |first11=Shu Ping |s2cid=9055313 |title=Deep Ultraviolet Photoluminescence of Water-Soluble Self-Passivated Graphene Quantum Dots |journal=ACS Nano |date=2014 |volume=8 |issue=6 |pages=6312–6320 |doi=10.1021/nn300760g|pmid=22559247 }}</ref>
<ref name="thej2014">{{cite news |publisher=The Journal.ie |title=Global breakthrough: Irish scientists discover how to mass produce 'wonder material' graphene |url=http://www.thejournal.ie/graphene-irish-researchers-major-breakdown-mass-production-1424843-Apr2014/ |date=20 April 2014 |access-date=20 December 2014}}</ref>
<ref name="zhu2014">{{cite journal |last1=Zhu |first1=Shou-En |last2=Yuan |first2=Shengjun |last3=Janssen |first3=G. C. A. M. |title=Optical transmittance of multilayer graphene |journal=EPL |date=1 October 2014 |volume=108 |issue=1 |page=17007 |doi=10.1209/0295-5075/108/17007 |arxiv=1409.4664 |bibcode=2014EL....10817007Z|s2cid=73626659 }}</ref>
<ref name="manch2014f">{{cite web |title=New £60m Engineering Innovation Centre to be based in Manchester |url=https://www.manchester.ac.uk/discover/news/new-60m-engineering-innovation-centre-to-be-based-in-manchester/ |website=The University of Manchester |date=10 September 2014 }}</ref>
<ref name="canew2015">{{cite web |url=http://www.cambridge-news.co.uk/Cambridge-Nanosystems-opens-new-factory/story-26705678-detail/story.html |archive-url=https://web.archive.org/web/20150923200122/http://www.cambridge-news.co.uk/Cambridge-Nanosystems-opens-new-factory/story-26705678-detail/story.html |url-status=dead |archive-date=2015-09-23 |title=Cambridge Nanosystems opens new factory for commercial graphene production |work=Cambridge News}}</ref>
<ref name="lizhi2015">{{cite journal|last1=Li|first1=Zhilin|last2=Chen|first2=Lianlian|last3=Meng|first3=Sheng|last4=Guo|first4=Liwei|last5=Huang|first5=Jiao|last6=Liu|first6=Yu|last7=Wang|first7=Wenjun|last8=Chen|first8=Xiaolong|date=2015|title=Field and temperature dependence of intrinsic diamagnetism in graphene: Theory and experiment|journal=Phys. Rev. B|volume=91|issue=9|page=094429|bibcode=2015PhRvB..91i4429L|doi=10.1103/PhysRevB.91.094429|s2cid=55246344}}</ref>
<ref name="zdet2015">{{cite journal |last1=Zdetsis |first1=Aristides D. |last2=Economou |first2=E. N. |title=A Pedestrian Approach to the Aromaticity of Graphene and Nanographene: Significance of Huckel's (4 n +2)π Electron Rule |journal=The Journal of Physical Chemistry C |date=23 July 2015 |volume=119 |issue=29 |pages=16991–17003 |doi=10.1021/acs.jpcc.5b04311 }}</ref>
<ref name="harris2018">{{cite journal |last1=Harris |first1=Peter |title=Transmission Electron Microscopy of Carbon: A Brief History |journal=C |date=12 January 2018 |volume=4 |issue=1 |pages=4 |doi=10.3390/c4010004 |doi-access=free }}</ref>
<ref name="dixit2019">{{cite journal |last1=Dixit |first1=Vaibhav A. |last2=Singh |first2=Yashita Y. |title=How much aromatic are naphthalene and graphene? |journal=Computational and Theoretical Chemistry |volume=1162 |pages=112504 |date=June 2019 |doi=10.1016/j.comptc.2019.112504|s2cid=196975315 }}</ref>
<ref name="cao2020">{{cite journal|last=Cao|first=K.|date=2020|title=Elastic straining of free-standing monolayer graphene|journal=Nature Communications|volume=11|issue=284|page=284|bibcode=2020NatCo..11..284C|doi=10.1038/s41467-019-14130-0|pmc=6962388|pmid=31941941}}</ref>
</references>

== External links ==
{{commons category}}

* [http://www.graphene.manchester.ac.uk/ Manchester's Revolutionary 2D Material] at ''[[The University of Manchester]]''
* [http://www.periodicvideos.com/videos/mv_graphene.htm Graphene] at ''[[The Periodic Table of Videos]]'' (University of Nottingham)
* [http://www.bbc.co.uk/news/science-environment-20975580 Graphene: Patent surge reveals global race]
* [https://www.cdc.gov/niosh/surveyreports/pdfs/356-12a.pdf 'Engineering Controls for Nano-scale Graphene Platelets During Manufacturing and Handling Processes' (PDF)]
* [https://nanohub.org/resources/723/download/2004.10.20-l21-ece453.pdf Band structure of graphene (PDF).]

{{Allotropes of carbon}}
{{emerging technologies|topics=yes|robotics=yes|manufacture=yes|materials=yes}}
{{Molecules detected in outer space}}

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{{Use dmy dates|date=January 2015}}

[[Category:Graphene| ]]
[[Category:Aromatic compounds]]
[[Category:Two-dimensional nanomaterials]]
[[Category:Quantum lattice models]]
[[Category:Quantum phases]]
[[Category:Group IV semiconductors]]
[[Category:Superhard materials]]
[[Category:Articles containing video clips]]
[[Category:21st-century inventions]]
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