View source for Rashba–Edelstein effect

{{distinguish|text=the [[Rashba effect|Bychkov–Rashba effect]], sometimes also known as the Rashba effect}}
{{Copy edit|date=October 2024}}
[[File:Rashba-splitted and topological insulator bands.png|thumb|400px|Rashba-splitted and topological insulator energy dispersion relations and Fermi contours: energy dispersion relation section (a) and Fermi contours (b) produced by the Rashba effect and energy dispersion relation section (c) and Fermi contour (d) at the topological insulator surface.<ref name="ZucchettiPhD" />]]

The '''Rashba–Edelstein effect''' ('''REE''') is a [[spintronics]]-related effect, consisting in the conversion of a bidimensional [[Electric current|charge current]] into a [[Spin (physics)|spin]] accumulation.<ref name="ZucchettiPhD">{{cite journal |last1=Zucchetti |first1=Carlo |title=Spin-charge interconversion in Ge-based structures |website=www.politesi.polimi.it |date=2019 |hdl=10589/145725 }}</ref><ref name="RojasSanchez2016">{{cite journal |last1=Rojas-Sánchez |first1=J.-C. |last2=Oyarzún |first2=S. |last3=Fu |first3=Y. |last4=Marty |first4=A. |last5=Vergnaud |first5=C. |last6=Gambarelli |first6=S. |last7=Vila |first7=L. |last8=Jamet |first8=M. |last9=Ohtsubo |first9=Y. |last10=Taleb-Ibrahimi |first10=A. |last11=Le Fèvre |first11=P. |last12=Bertran |first12=F. |last13=Reyren |first13=N. |last14=George |first14=J.-M. |last15=Fert |first15=A. |title=Spin-pumping into surface states of topological insulator α-Sn, spin to charge conversion at room temperature |journal=Physical Review Letters |date=1 March 2016 |volume=116 |issue=9 |page=096602 |doi=10.1103/PhysRevLett.116.096602|pmid=26991190 |arxiv=1509.02973 |s2cid=91173907 }}</ref> This effect is an [[Intrinsic and extrinsic properties|intrinsic]] charge-to-spin conversion mechanism<ref name="ZucchettiPhD" /> and it was predicted in 1990 by the scientist V.M. Edelstein.<ref name="Edelstein1990">{{cite journal |last1=Edelstein |first1=V.M. |title=Spin polarization of conduction electrons induced by electric current in two-dimensional asymmetric electron systems |journal=Solid State Communications |date=January 1990 |volume=73 |issue=3 |pages=233–235 |doi=10.1016/0038-1098(90)90963-C|bibcode=1990SSCom..73..233E }}</ref> It has been demonstrated in 2013<ref name="RojasSanchez2013">{{cite journal |last1=Rojas-Sánchez |first1=J. C.  |last2=Vila |first2=L. |last3=Desfonds |first3=G. |last4=Gambarelli |first4=S. |last5=Attané |first5=J. P. |last6=De Teresa |first6=J. M. |last7=Magén |first7=C. |last8=Fert |first8=A. |title=Spin-to-charge conversion using Rashba coupling at the interface between non-magnetic materials |journal=Nature Communications |date=17 December 2013 |volume=4 |issue=1 |page=2944 |doi=10.1038/ncomms3944|pmid=24343336 |bibcode=2013NatCo...4.2944S |doi-access=free }}</ref> and confirmed by several experimental evidences in the following years.<ref name="RojasSanchez2016" /><ref name="Zhang2015">{{cite journal |last1=Zhang |first1=H. J. |last2=Yamamoto |first2=S. |last3=Gu |first3=B. |last4=Li |first4=H. |last5=Maekawa |first5=M. |last6=Fukaya |first6=Y. |last7=Kawasuso |first7=A. |title=Charge-to-Spin Conversion and Spin Diffusion in Bi/Ag Bilayers Observed by Spin-Polarized Positron Beam |journal=Physical Review Letters |date=22 April 2015 |volume=114 |issue=16 |page=166602 |doi=10.1103/PhysRevLett.114.166602|pmid=25955066 |bibcode=2015PhRvL.114p6602Z }}</ref><ref name="Mellnik2014">{{cite journal |last1=Mellnik |first1=A. R. |last2=Lee |first2=J. S. |last3=Richardella |first3=A. |last4=Grab |first4=J. L. |last5=Mintun |first5=P. J. |last6=Fischer |first6=M. H. |last7=Vaezi |first7=A. |last8=Manchon |first8=A. |last9=Kim |first9=E.-A. |last10=Samarth |first10=N. |last11=Ralph |first11=D. C. |s2cid=205239604 |title=Spin-transfer torque generated by a topological insulator |journal=Nature |date=23 July 2014 |volume=511 |issue=7510 |pages=449–451 |doi=10.1038/nature13534|pmid=25056062 |arxiv=1402.1124 |bibcode=2014Natur.511..449M }}</ref><ref name="RE detection using Josephson junction">{{cite journal |last1=Senapati |first1=Tapas |last2=Karnad |first2=Ashwin Kumar |last3=Senapati |first3=Kartik |title=Phase biasing of a Josephson junction using Rashba–Edelstein effect |journal=Nature Communications |date=16 November 2023 |volume=14 |issue=1 |page=7415 |doi=10.1038/s41467-023-42987-9|pmid=37973986 |pmc=10654735 |arxiv=2304.11457 }}</ref>

Its origin can be ascribed to the presence of spin-polarized surface or interface states.<ref name="Bottegoni-NuovoCimento">{{cite journal |last1=Bottegoni |first1=F. |last2=Zucchetti |first2=C. |last3=Isella |first3=G. |last4=Bollani |first4=M. |last5=Finazzi |first5=M. |last6=Ciccacci |first6=F. |s2cid=214054493 |title=Spin-charge interconversion in heterostructures based on group-IV semiconductors |journal=La Rivista del Nuovo Cimento |date=17 February 2020 |volume=43 |issue=2 |pages=45–96 |doi=10.1007/s40766-020-0002-0|bibcode=2020NCimR..43...45B |hdl=11311/1133071 |hdl-access=free }}</ref> Indeed, a structural inversion [[symmetry breaking]] (i.e., a structural inversion asymmetry (SIA)) causes the [[Rashba effect]] to occur: this effect breaks the spin degeneracy of the energy bands and it causes the spin polarization being locked to the momentum in each branch of the [[dispersion relation]].<ref name="RojasSanchez2016" /> If a charge current flows in these spin-polarized surface states, it generates a spin accumulation.<ref name="Bottegoni-NuovoCimento" /> In the case of a bidimensional Rashba gas, where this band splitting occurs,<ref name="Schliemann2003">{{cite journal |last1=Schliemann |first1=John |last2=Loss |first2=Daniel |s2cid=119093889 |title=Anisotropic transport in a two-dimensional electron gas in the presence of spin-orbit coupling |journal=Physical Review B |date=14 October 2003 |volume=68 |issue=16 |page=165311 |doi=10.1103/PhysRevB.68.165311|arxiv=cond-mat/0306528 |bibcode=2003PhRvB..68p5311S }}</ref> this effect is called ''' Rashba–Edelstein effect'''.<ref name="ZucchettiPhD" /><ref name="Bottegoni-NuovoCimento" />

For what concerns a class of peculiar materials, called [[Topological insulator|topological insulators (TI)]], spin-splitted surface states exist due to the surface topology, independently from the Rashba effect.<ref name="Gambardella2011" /> Topological insulators, indeed, display a spin-splitted linear [[dispersion relation]] on their surfaces (i.e., spin-polarized [[Dirac cone]]s<ref name="Hasan2010">{{cite journal |last1=Hasan |first1=M. Z. |last2=Kane |first2=C. L. |s2cid=16066223 |title=Colloquium: Topological insulators |journal=Reviews of Modern Physics |date=8 November 2010 |volume=82 |issue=4 |pages=3045–3067 |doi=10.1103/RevModPhys.82.3045|arxiv=1002.3895 |bibcode=2010RvMP...82.3045H }}</ref>), while having a band gap in the bulk (this is why these materials are called insulators).<ref name="ZucchettiPhD" /> Also in this case, spin and momentum are locked<ref name="RojasSanchez2016" /> and, when a charge current flows in these spin-polarized surface states, a spin accumulation is produced and this effect is called '''Edelstein effect'''.<ref name="Bottegoni-NuovoCimento" /> In both cases, a 2D charge-to-spin conversion mechanism occurs.<ref name="Bottegoni-NuovoCimento" />

The reverse process is called the inverse Rashba–Edelstein effect and it converts a spin accumulation into a bidimensional charge current, resulting in a 2D spin-to-charge conversion.<ref name="Isasa2016">{{cite journal |last1=Isasa |first1=Miren |last2=Martínez-Velarte |first2=M. Carmen |last3=Villamor |first3=Estitxu |last4=Magén |first4=César |last5=Morellón |first5=Luis |last6=De Teresa |first6=José M. |last7=Ibarra |first7=M. Ricardo |last8=Vignale |first8=Giovanni |last9=Chulkov |first9=Evgueni V. |last10=Krasovskii |first10=Eugene E. |last11=Hueso |first11=Luis E. |last12=Casanova |first12=Fèlix |s2cid=398872 |title=Origin of inverse Rashba–Edelstein effect detected at the Cu/Bi interface using lateral spin valves |journal=Physical Review B |date=13 January 2016 |volume=93 |issue=1 |page=014420 |doi=10.1103/PhysRevB.93.014420|bibcode=2016PhRvB..93a4420I |hdl=10261/136761 |hdl-access=free }}</ref>

The Rashba–Edelstein effect and its inverse effect are classified as a spin-charge interconversion (SCI) mechanisms, as the direct and inverse [[spin Hall effect]], and materials displaying these effects are promising candidates for becoming spin injectors, detectors and for other future technological applications.<ref name="ZucchettiPhD" /><ref name="RojasSanchez2016" /><ref name="RojasSanchez2013" />

The Rashba–Edelstein effect is a surface effect, at variance with the spin Hall effect which is a bulk effect.<ref name="ZucchettiPhD" /> Another difference among the two, is that the Rashba–Edelstein effect is a purely intrinsic mechanism, while the spin Hall effect origin can be either intrinsic or extrinsic.<ref name="Dyakonov2008">{{cite book |last1=Dyakonov |first1=Mikhail I. |title=Spin physics in semiconductors |date=2008 |publisher=Springer |isbn=978-3-540-78819-5}}</ref>

==Physical origin==

The origin of the Rashba–Edelstein effect relies on the presence of spin-split surface or interface states, which can arise for a structural inversion asymmetry or because the material exhibits a topologically protected surface, being a topological insulator.<ref name="ZucchettiPhD" /><ref name="Bottegoni-NuovoCimento" /> In both cases, the material surface displays the spin polarization locked to the momentum, meaning that these two quantities are univocally linked and orthogonal one to the other (this is clearly visible from the [[Fermi surface|Fermi countours]]).<ref name="ZucchettiPhD" /><ref name="Bottegoni-NuovoCimento" /><ref name="Gambardella2011" /><ref name="Hasan2010" /> It is worth noticing that also a bulk inversion asymmetry could be present, which would result in the [[Dresselhaus effect]].<ref name="ZucchettiPhD" /> In fact, if, in addition to the spatial inversion asymmetry or to the topological insulator band structure, also a bulk inversion asymmetry is present, the spin and momentum are still locked but their relative orientation is not straightforwardly determinable (since also the orientation of the charge current with respect to the crystallographic axes plays a relevant role).<ref name="Gambardella2011" /> In the following discussion, the Dresselhaus effect will be neglected, for simplicity.<ref name="Gambardella2011" />

[[File:Edelstein effect topological insulators.png|thumb|500px|Topological insulator band structure in equilibrium (a) and in a non equilibrium situation, when a spin-charge interconversion process occurs (b). Two possible effects could lead to the non-equilibrium situation: the injection of a charge current (i.e., a momentum unbalance) which is converted into a spin accumulation (Edelstein effect) or the injection of spins, resulting in a spin accumulation that produces a charge current (inverse Edelstein effect).<ref name="ZucchettiPhD" />]]

The topological insulator case is easier to visualize due to the presence of a single Fermi contour, therefore the topological insulator case is discussed first. [[Topological insulator]]s display spin-split surface states where spin-momentum locking is present.<ref name="ZucchettiPhD" /><ref name="RojasSanchez2016" /><ref name="Hasan2010" /> Indeed, when a charge current flows in the surface states of the topological insulator, it can also be seen as a well-defined momentum shift <math>\Delta k</math> in the [[reciprocal space]], resulting in a different occupation of the spin-polarized branches of the Dirac cone.<ref name="ZucchettiPhD" /> This unbalance, according to the structure of the topological insulator band dispersion relation, produces a spin accumulation in the investigated material, i.e., a charge-to-spin conversion occurs.<ref name="Edelstein1990" /> The spin accumulation is orthogonal to the injected charge current, accordingly to spin-momentum locking.<ref name="Shen2014a">{{cite journal |last1=Shen |first1=Ka |last2=Vignale |first2=G. |last3=Raimondi |first3=R. |s2cid=29825170 |title=Microscopic Theory of the Inverse Edelstein Effect |journal=Physical Review Letters |date=5 March 2014 |volume=112 |issue=9 |page=096601 |doi=10.1103/PhysRevLett.112.096601|pmid=24655266 |arxiv=1311.6516 |bibcode=2014PhRvL.112i6601S }}</ref> Due to the fact that these materials display a conductive behaviour on their surface while being insulating on their bulk, the charge current is only allowed to flow on the topological insulator surfaces: this is the origin of the bidimensionality of this charge-to-spin conversion mechanism.<ref name="ZucchettiPhD" /><ref name="Cai2018">{{cite journal |last1=Cai |first1=Shu |last2=Guo |first2=Jing |last3=Sidorov |first3=Vladimir A. |last4=Zhou |first4=Yazhou |last5=Wang |first5=Honghong |last6=Lin |first6=Gongchang |last7=Li |first7=Xiaodong |last8=Li |first8=Yanchuan |last9=Yang |first9=Ke |last10=Li |first10=Aiguo |last11=Wu |first11=Qi |last12=Hu |first12=Jiangping |last13=Kushwaha |first13=Satya. K. |last14=Cava |first14=Robert J. |last15=Sun |first15=Liling |s2cid=119366200 |title=Independence of topological surface state and bulk conductance in three-dimensional topological insulators |journal=npj Quantum Materials |date=23 November 2018 |volume=3 |issue=1 |page=62 |doi=10.1038/s41535-018-0134-z|arxiv=1807.02000 |bibcode=2018npjQM...3...62C }}</ref>

For what concerns the Rashba–Edelstein effect, the spin-split dispersion relation consists in two bands displaced along the ''k''-axis due to a structural inversion asymmetry (SIA), accordingly to the [[Rashba effect]] (i.e., these bands show a linear splitting in ''k'' due to the [[Spin–orbit interaction|spin-orbit coupling]]<ref name="Gambardella2011">{{cite journal |last1=Gambardella |first1=Pietro |last2=Miron |first2=Ioan Mihai |s2cid=29025534 |title=Current-induced spin–orbit torques |journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |date=13 August 2011 |volume=369 |issue=1948 |pages=3175–3197 |doi=10.1098/rsta.2010.0336|pmid=21727120 |bibcode=2011RSPTA.369.3175G |doi-access= }}</ref><ref name=Manchon2015>{{cite journal |last1=Manchon |first1=A. |last2=Koo |first2=H. C. |last3=Nitta |first3=J. |last4=Frolov |first4=S. M. |last5=Duine |first5=R. A. |s2cid=24116488 |title=New perspectives for Rashba spin–orbit coupling |journal=Nature Materials |date=20 August 2015 |volume=14 |issue=9 |pages=871–882 |doi=10.1038/nmat4360|pmid=26288976 |arxiv=1507.02408 |bibcode=2015NatMa..14..871M }}</ref>). This results in two [[Fermi surface|Fermi countours]], which are concentric at equilibrium, both displaying spin-momentum locking but with opposite [[Helicity (particle physics)|helicity]].<ref name="Gambardella2011" /> If the system is driven in an out-of-equilibrium condition by injecting a charge current, the two disk displace one from the other and a net spin accumulation arises.<ref name="Gambardella2011" /> This effect occurs, for instance, in a bidimensional Rashba gas.<ref name="ZucchettiPhD" /> The Rashba splitting complicates the understanding and the visualization of the spin-to-charge conversion mechanism but the basic working principle of the Rashba–Edelstein effect is very similar to the one of the Edelstein effect.<ref name="ZucchettiPhD" /><ref name="RojasSanchez2013" />

Experimentally speaking, the Rashba–Edelstein effect occurs if a charge current is electrically injected inside the topological insulator, for instance by means of two electrodes where a [[Voltage|potential difference]] is applied. The resulting spin accumulation can be probed in several ways, one of them is by employing the [[Kerr effect#Magneto optical Kerr effect|magneto optical Kerr effect (MOKE)]].<ref name="ZucchettiPhD" />

==Inverse Rashba–Edelstein effect==

The reverse process, i.e., the inverse Rashba–Edelstein effect (I(R)EE)<ref name="Shen2014a" /> occurs when a spin accumulation is generated inside the investigated material and a consequent charge current arises on the material surface (in this case, we have a 2D spin-to-charge conversion).<ref name="ZucchettiPhD" /> In order to have the inverse Rashba–Edelstein effect, a spin accumulation is required to be generated inside the analyzed material, and this spin injection is usually achieved by coupling the material under investigation with a ferromagnet in order to perform the [[spin pumping]]<ref name="RojasSanchez2016" /><ref name="Xu2016">{{cite book |last1=Xu |first1=Yongbing |last2=Awschalom |first2=David D. |last3=Nitta |first3=Junsaku |title=Handbook of spintronics |date=11 March 2016 |isbn=978-94-007-6893-2 |pages=1–1596 |publisher=Springer |edition=1st. 2016}}</ref> or with a semiconductor where it is possible to perform optical orientation.<ref name="Lampel1968">{{cite journal |last1=Lampel |first1=Georges |title=Nuclear Dynamic Polarization by Optical Electronic Saturation and Optical Pumping in Semiconductors |journal=Physical Review Letters |date=4 March 1968 |volume=20 |issue=10 |pages=491–493 |doi=10.1103/PhysRevLett.20.491|bibcode=1968PhRvL..20..491L }}</ref><ref name="Meier1984">{{cite book |last1=Meier |first1=F. |last2=Zakharchenya |first2=B.P. |title=Optical Orientation |date=1 November 1984 |publisher=Elsevier Science |isbn=9780444599919}}</ref><ref name="Dyakonov1984">{{cite book |last1=Dyakonov |first1=Michel |last2=Perel |first2=Valerie |title=Optical Orientation |chapter=Theory of Optical Spin Orientation of Electrons and Nuclei in Semiconductors |series=Modern Problems in Condensed Matter Sciences |date=1984 |volume=8 |pages=11–71 |doi=10.1016/B978-0-444-86741-4.50007-X|isbn=9780444867414 }}</ref> As for the direct effect, the inverse Rashba–Edelstein effect occurs in materials lacking the structural inversion symmetry, while in topological insulators the inverse Edelstein effect arises.<ref name="ZucchettiPhD" />

In the case of the inverse Edelstein effect, by looking at the section of the [[Dirac cone]], the spin-to-charge conversion can be visualized as follows: the spin injection produces a piling up of spins of one character in one of the energy dispersion relation branches.<ref name="ZucchettiPhD" /><ref name="Bottegoni-NuovoCimento" /> This results in a spin unbalance due to the different branch occupations (i.e., a spin accumulation), which leads to a momentum unbalance and, therefore, to a charge current which can be electrically probed.<ref name="Bottegoni-NuovoCimento" /> As for the direct effect, also in the inverse Edelstein effect, the charge current can only flow on the topological insulator surfaces due to the energy band conformation.<ref name="Hasan2010" /> This is how the 2D spin-to-charge conversion occurs in these materials and this could allow topological insulators to be exploited as spin detectors.<ref name="RojasSanchez2016" />

As for the direct effect, this analysis has been carried out for the inverse Edelstein effect because in this case only two energy branches are present. For what concerns the inverse Rashba–Edelstein effect, the process is very similar despite the presence of four energy branches, with spin-momentum locking, in the dispersion relation and two consequent Fermi countours with opposite helicity.<ref name="ZucchettiPhD" /><ref name="Bottegoni-NuovoCimento" /> In this case, the two Fermi countours, when a spin accumulation is generated inside the material, will be displaced one from the other, generating a charge current, at variance with the equilibrium case in which the two Fermi countours are concentric and no net momentum unbalance nor spin accumulation are present.<ref name="ZucchettiPhD" /><ref name="Gambardella2011" />

==Process efficiency==

While both the Rashba–Edelstein effect and the inverse Rashba–Edelstein effect rely on a spin accumulation, the figure of merit of the processes is commonly computed by accounting for the spin current density related to the spin accumulation, instead of the spin accumulation itself, in analogy with the spin Hall angle for the spin Hall effect.<ref name="RojasSanchez2016" /> Indeed, the efficiency of the Rashba–Edelstein effect and of the inverse Rashba–Edelstein effect can be estimated by means of the Rashba–Edelstein length, i.e., the ratio between the charge current density, flowing on the surface of the investigated material, (i.e., a surface charge current density) and the three-dimensional spin current density (since the spin accumulation can [[Spin diffusion|diffuse]] in the three-dimensional space).<ref name="RojasSanchez2016" />

In the Rashba–Edelstein effect the spin current is a consequence of the spin accumulation that occurs in the material as the charge current flows on its surface (under the influence of a potential difference and, therefore, of an electric field), while in the inverse Rashba–Edelstein effect the spin current is the quantity injected inside the material leading to a spin accumulation and resulting in a charge flow localized at the material surface.<ref name="ZucchettiPhD" /><ref name="Bottegoni-NuovoCimento" /> In both cases, the asymmetry in the charge and spin current dimensions results in a ratio which dimensionally has the units of a length: this is the origin of the name of this efficiency parameter.<ref name="ZucchettiPhD" />

Analytically, the value of the bidimensional charge current density can be computed employing the [[Boltzmann equation]] and considering the action of an electric field <math>\mathbf{E}</math>, resulting in:<ref name="ZucchettiPhD" /><ref name="Gambardella2011" />
:<math>\mathbf{j} = -\frac{q^2 \tau_{\rm m} k_{\rm F} v_{\rm F}}{4 \pi^2 \hbar}\mathbf{E}</math>,
where <math>q</math> is the elementary charge, <math>\tau_{\rm m}</math> is the momentum scattering time, <math>k_{\rm F}</math> and <math>v_{\rm F}</math> are, respectively, the [[Fermi energy#Related quantities|Fermi wavevector]]  and the [[Fermi energy#Related quantities|Fermi velocity]] and <math>\hbar</math> is the reduced [[Planck constant]]. 
The spin current density can be also analytically computed by integrating across the Fermi surface the product of the spin polarization and the corresponding [[Distribution function (physics)|distribution function]].
In the Edelstein effect case, this quantity results in:<ref name="ZucchettiPhD" /><ref name="Gambardella2011" />
:<math>\mathbf{j_{s}} = -\frac{q^2 k_{\rm F}}{4 \pi^2 \hbar}\mathbf{E}\times\mathbf{n}</math>,
where <math>\mathbf{n}</math> is the unit vector perpendicular to the surface on which the charge current flows.
From these formula it can be observed the orthogonality of the spin and the charge current densities.<ref name="ZucchettiPhD" />

For what regards the Edelstein and its inverse effects, the conversion efficiency is:<ref name="ZucchettiPhD" />
:<math>\lambda_{\rm EE} = \frac{j}{j_{s}} = \tau_{\rm m} v_{\rm F}</math>.<ref name="ZucchettiPhD" /><ref name="RojasSanchez2016" /> 
This parameter is conventionally positive for a Fermi contour with a counterclockwise helicity.<ref name="RojasSanchez2016" /> The Rashba–Edelstein length derivation is the same as the Edelstein one, except for <math>v_{\rm F}</math> which is substituted by the [[Rashba effect#Hamiltonian|Rashba parameter]] <math>\alpha_{\rm R}</math>,<ref name="Gambardella2011" /> i.e., <math>v_{\rm F} \to \frac{\alpha_{\rm R}}{\hbar}</math>, resulting in:<ref name="ZucchettiPhD" />
:<math>\lambda_{\rm REE} = \frac{j}{j_{s}} = \frac{\tau_{\rm m} \alpha_{\rm R}}{\hbar}</math>.

The Rashba–Edelstein length of the investigated material can be compared to other spin-charge interconversion efficiencies,<ref name="RojasSanchez2016" /> as the spin-Hall angle,<ref name="ZucchettiPhD" /> to establish if this material is an efficient spin-charge interconverter, and, therefore, if it could be suitable for spintronic applications.<ref name="RojasSanchez2016" /> The Rashba–Edelstein length (2D spin-charge interconversion efficiency) can be effectively compared to the spin Hall angle (3D spin-charge interconversion efficiency), by dividing the <math>\lambda_{\rm REE}</math> parameter for the thickness of the spin-splitted surface states in which this 2D conversion occurs.<ref name="RojasSanchez2013" /> This "equivalent" spin Hall angle for the Rashba–Edelstein effect often results in being close to the unity or even greater than the unity:<ref name="RojasSanchez2013" /> the Rashba–Edelstein effect, on average, is a more efficient spin-charge interconversion mechanism than the spin Hall effect and this could lead to a future employment of materials displaying this effect in the technological industry.<ref name="RojasSanchez2016" /><ref name="RojasSanchez2013" /><ref name="Ghiasi2019">{{cite journal |last1=Ghiasi |first1=Talieh S. |last2=Kaverzin |first2=Alexey A. |last3=Blah |first3=Patrick J. |last4=van Wees |first4=Bart J. |title=Charge-to-Spin Conversion by the Rashba–Edelstein Effect in Two-Dimensional van der Waals Heterostructures up to Room Temperature |journal=Nano Letters |date=13 August 2019 |volume=19 |issue=9 |pages=5959–5966 |doi=10.1021/acs.nanolett.9b01611|arxiv=1905.01371 |pmid=31408607 |pmc=6746057 |bibcode=2019NanoL..19.5959G }}</ref>

== See also ==

*[[Spin Hall effect]]
*[[Topological insulator]]
*[[Rashba effect]]
*[[Dresselhaus effect]]
*[[Spintronics]]

== References ==
{{reflist}}

{{DEFAULTSORT:Rashba-Edelstein effect}}
[[Category:Condensed matter physics]]
[[Category:Spintronics]]
[[Category:Semiconductors]]
[[Category:Quantum magnetism]]