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1_00 Nature physics 2013 - Zeeman-type spin splitting controlled by an electric field
导读：Zeeman-typespinsplittingcontrolledbyanelectric?eldHongtaoYuan1,2*,MohammadSaeedBahramy1,3*,KazuhiroMorimoto1,SanfengWu4,KentaroNomura3,5,Bohm-JungYang3,HidekazuShimotani1,6,RyujiSu
Zeeman-typespinsplittingcontrolledbyanelectric?eld
HongtaoYuan1,2*,MohammadSaeedBahramy1,3*,KazuhiroMorimoto1,SanfengWu4,KentaroNomura3,5,Bohm-JungYang3,HidekazuShimotani1,6,RyujiSuzuki1,MinglinToh7,ChristianKloc7,XiaodongXu4,8,RyotaroArita1,3,NaotoNagaosa1,3andYoshihiroIwasa1,3*
Transition-metaldichalcogenidessuchasWSe2andMoS2haveelectronicbandstructuresthatareidealforhostingmanyexoticspin–orbitphenomena.HereweinvestigatethepossibilitytogenerateandmodulateagiantZeeman-typespinpolarizationinWSe2underanexternalelectric?eld.Bytuningtheperpendicularelectric?eldappliedtotheWSe2channelwithanelectric-double-layertransistor,weobserveasystematiccrossoverfromweaklocalizationtoweakanti-localizationinmagnetotransport.Ouropticalre?ectionmeasurementsalsorevealanelectricallytunableexcitonsplitting.Using?rst-principlescalculations,weproposethattheseareprobablyduetotheemergenceofamerelyout-of-planeandmomentum-independentspinsplittingatandinthevicinityoftheverticesoftheWSe2Brillouinzoneunderelectric?eld.Thenon-magneticapproachforcreatingsuchanintriguingspinsplittingkeepsthesystemtime-reversallyinvariant,therebysuggestinganewmethodformanipulatingthespindegreesoffreedomofelectrons.
pin–orbitinteraction(SOI)isarelativisticeffectoriginatingfromthecouplingofaparticle’sspinsandmomentumpunderanexternalelectricfieldE,asdescribedbytheSOI
?so=?μBσ·(p×E/2mc2),whereσ,μB,mandcHamiltonianH
arespinPaulimatrices,theBohrmagneton,theeffectivemassofcarriersandthevelocityoflight,respectively.Intheabsenceofinversionsymmetry,SOIliftsthespindegeneracyofelectronicstatesatgenerick-pointsintheBrillouinzone,leadingtointerestingeffectssuchasthespinHalleffect1,thespin-galvaniceffect2and
?so,thestrengthofspinballistictransport3.AsisevidentfromH
theeffectivemagneticfieldBeff=(p×E/2mc2)anditsresultingspinpolarizationiscruciallydependentonbothpandEandtheirrelativedirections4,5.OnepossiblewaytoregulateBeffistocreateanon-centrosymmetricpotentialwellatsemiconductorheterointerfacesbyapplyinganexternalelectricfieldEex.montoallofthesesystemsisaRashba-typespinsplitting(asschematizedinFig.1a)ofenergybandsaroundthehigh-symmetryk-pointsoftheBrillouinzone(forexample,the??-point)withamomentum-paredwithsuchanin-planeRashba-typespinpolariza-tion,theelectricalgenerationofout-of-planeZeeman-typespinpolarization,asdepictedinFig.1b,hasprovedtobeachallengingtask.Thisismainlybecausetheelectron/holepocketsareusuallyformedaroundtime-reversalk-points(forexample,the??-point),wheresuchaspinpolarizationissymmetry-forbidden,unlessthetime-reversalsymmetryisbroken,forinstance,byanexternalmag-neticfieldormagneticdopants.Furthermore,iftheFermisurfaceiscentredatalow-symmetrick-point,theresultingspintextureisoftenveryirregular.Inthispaper,weinvestigatethepossibilityofelectricallyinducingsuchanout-of-planeZeeman-likespinpolarizationusingionic-liquid-gatedfield-biningtheelectronictransportandopticalexperiments,weobserveanelectric-field-modulatedcrossoverfromweaklocalization(WL)toweakanti-localization(WAL)inmagnetoconductanceaswellasatunableexcitonsplittingintheopticalspectraofWSe2.Usingfirst-principlescalculationsweproposethattheseobservationsaremostlikelyduetoanelectric-field-inducedout-of-planeZeeman-likespinpolarization.Suchaspinpolarizationistheoreticallyshowntotakeplaceatandinthevicinityofspeciallow-symmetrick-pointsatthecorners(K-points)ofthehexagonalBrillouinzoneofWSe2withanalternatingsignbetweentheoppositecorners(KandK??points)duetothetime-reversalinvarianceofthesystem.Ourcalculationssuggestthattheresultingspinsplittingistunableandcanreach300meV,comparabletothelargestvaluesofspinsplittingreportedforRashbasystems7–11.
UsingWSe2single-crystalflakes,wehavefabricatedanelectric-double-layertransistor(EDLT).TheadvantageoftheEDLTisthatitcangeneratealargeinterfacialelectricfield(upto50MVcm?1or0.5eV??1),enablingahighdensitycarrieraccumulationatliquid/solidinterfaces14–20withtunableinversionasymmetry.Wechose2H–WSe2because:ithostsheavy5delementswithstrongatomicSOI(about450meV,muchstrongerthanthatinthemoreintensivelystudiedMoS2system21,22);itcanbecleavedintoatomicallyflatsurfaces,andthusisanaturallygoodcandidateforbeiandithasauniqueelectronicbandstructurewithtwonearlyenergy-degeneratevalencebandmaximaattwodifferentpointsoftheBrillouinzonewithdistinctsymmetry
1Quantum-Phase
ElectronicsCenterandDepartmentofAppliedPhysics,TheUniversityofTokyo,Tokyo113-8656,Japan,2GeballeLaboratoryfor
AdvancedMaterials,StanfordUniversity,Stanford,California94305,USA,3RIKENCenterforEmergentMatterScience(CEMS),Wako351-0198,Japan,4DepartmentofPhysics,UniversityofWashington,Seattle,Washington98195,USA,5InstituteforMaterialsResearch,TohokuUniversity,Sendai980-8577,Japan,6DepartmentofPhysics,TohokuUniversity,Sendai980-8578,Japan,7SchoolofMaterialsScienceandEngineering,Nanyang
TechnologicalUniversity,639-798,Singapore,8DepartmentofMaterialScienceandEngineering,UniversityofWashington,Seattle,Washington98195,USA.*e-mail:htyuan@ap.t.u-tokyo.ac.bahramy@ap.t.u-tokyo.ac.iwasa@ap.t.u-tokyo.ac.jp
NATUREPHYSICS|VOL9|SEPTEMBER2013|/naturephysics
In-Diplanpoe le
Mirror plane
E ? EVBM (eV)
0?1?2?3?4?5
Figure1|RashbaeffectversusZeemaneffectandtheelectronicstructureofbulk2H–WSe2.a,b,Schematicsrepresentingin-planeRashba-typespinpolarization(a)andout-of-planeZeeman-typespinpolarization(b).Theappliedelectric?eldEex(verticalgreenarrows)isperpendiculartothe2Dplanewherethecarriersarecon?ned.TheyellowplanerepresentstheFermilevel.c,Sideandtopviewsofthelayeredstructureof2H–WSe2.d,Anetin-planedipolemomentcanbefoundattheW4+ionsduetotheD3hsymmetry(C3v+M)ofeachSe–W–Semonolayer.InthebilayerWSe2(oneunitcell),thesymmetrybecomesD46h,sothatthenetin-planedipoleinthewholeunitcellbecomeszero.Bottominset:theBrillouinzoneof2H–WSe2.e,Theelectronicbandstructureofbulk2H–WSe2.
properties.AsshowninFig.1e,thehighestvalence-bandmaximum(VBM)islocatedattheBrillouinzonecentre,the??-point,whereastheotherone,lyingatslightlylowerenergies,appearsattheK-point.Ofparticularimportance,WSe2hasa2Hb–MoS2-typecrystalstructure(D46hsymmetryandtheP63/mmcspacegroup).TheprimitivecellofWSe2iscomposedoftwoformulaunits.Withineachunit,oneWatomissandwichedbetweentwoSeatoms,therebyformingaSe–W–Semonolayerstackingnon-symorphicallyalongthecaxiswithD3hsymmetry(Fig.1c).OwingtotheD3hsymmetry,anetin-planeelectricdipolemomentcanlocallyactontheWatomswithineachmonolayer(Fig.1d),playingacrucialroleininducingtheout-of-planespinpolarization,aswillbeshownlater.
Figure2aisacross-sectionaldiagramofanionic-liquid-gatedWSe2EDLT.ThesheetconductanceσxxasafunctionofgatevoltageVGshowsawell-definedambipolartransport(Fig.2b).TheHallcoefficientRHdeducedfromHalleffectmeasurementsisfoundtobenegativeintheVGrangeof[?6Vto+6V]at220K(Fig.2c).Loweringthetemperatureto2K,RHchangessignundernegativeVGandbecomesunambiguouslypositive,indicatinghole(h+)accumulation.ThischangeinRHisattributedtothefreezingofresidualbulkelectronsthroughcooling23.Consistentwiththeσxx–VGplot,thesheetcarrierdensityns=1/(RH|e|)increaseswithincreasingbiasinbothdirections,andeventuallyshowsapeak-likebehaviour.Weestimatethemaximumdensityofaccumulatedholestobe1.9×1015cm?2at2K,correspondingto0.44h+perWatom(hereweassumethattheholeaccumulationisconfinedwithintheThomas–Fermiscreeninglength,whichis2.6nmorabouttwounitcells).Figure2dshowsthetemperaturedependenceofsheet
resistance(Rxx–Tplot)ofthehole-accumulatedWSe2channel.At|VG|&3.75V,thechannelshowsaninsulatingbehaviourwiththenegativetemperaturedependence.Furtherincreasingtheholeaccumulation,thechannelundergoesaninsulator–metaltransitionandbecomescompletelymetallicatVG=?5.0V.Incontrast,asindicatedinFig.2e,theelectronaccumulationdoesnotleadtoanyinsulator–metaltransitionevenatVG=+4.5Vowingtotheinsufficiencyofelectronsaccumulatedattheinterface(themaximumcarrierdensityis1.4×1014cm?2at220K).Hereafter,wethusfocusonlyonthenegativeVGregion.
AsaneffectivewayofdetectingtheSOIanditsfield-effectmodulation7–10,24–26,wehaveperformedmagneto-transportmea-surementstoprobethespinrelaxationprocessesinWSe2.Figure3ashowstheVGvariationofnormalizedmagnetoconduc-tance??σ/σ(0)oftheholeaccumulatedattheEDLTinterfaceat2K.Here??σisdefinedasσ(H)?σ(H=0),withσandHbeingthesheetconductanceandthemagneticfieldappliedper-pendiculartotheinterface.For|VG|&3.0V,weobserveapositivemagnetoconductance,indicatingadominantWL.BychangingVGfrom?3.5Vto?6V,asharpmagnetoconductancepeak,initiallyappearingasaspikefeature,quicklystartstogrowaroundH=0.Theappearanceofsuchanegativecusp-likemagnetoconductancepeakatlowtemperatures(thetemperaturedependenceisdemon-stratedforVG=?4.5VinSupplementaryFig.S1)isacharacteristicfeatureoftheWALregime,whereowingtothedominanceofSOI,thecarrierstravellingalongthetime-reversedclosedloopsinterferedestructively,leadingtothequantumenhancementofconductivity.Theobservationofelectric-field-dependentWALis
NATUREPHYSICS|VOL9|SEPTEMBER2013|/naturephysics
Pt gate electrode
Ionic liquid
Sheet conductance (mS)
PotentialVG (V)
Wave-function
RH (cm2 C?1)
25ns ( 1014 cm?2)
Figure2|ElectronictransportinaWSe2EDLTwithionicliquidgating.a,SchematicstructureofatypicalWSe2EDLT.ByapplyinganegativeVGthroughaPtgateelectrode,anionsintheionicliquidareelectrostaticallydriventotheWSe2surface,formingahighlychargedelectricdoublelayer(EDL)interface.MostofpotentialdropoccursattheEDLinterfaceandalmostnopotentialisdistributedintheliquid.b,Ambipolaroperationinthetransfercharacteristics(σxxversusVG)ofWSe2EDLTs,measuredat220Kwithasource–drainvoltageVDSof0.1V.c,Hallcoef?cientRHandsheetcarrierdensityns=1/RHeobtainedfromHallmeasurementsdirectlyindicateambipolartransportoftheWSe2channel.Reddotsindicateelectronaccumulationat220K;bluedotsindicateholeaccumulationat2K.Thegraduatedshadinginbandcrepresentstheamountandtypeofaccumulatedcarriersattheinterface(blueforholeandbrownforelectronaccumulation).d,Temperature-dependentRxxundervariousnegativeVGshowsanelectric-?eld-inducedinsulator–metaltransition.e,Temperature-dependentRxxmeasuredatvariouspositiveVGforelectronaccumulation.Nometallicstateisobtainedowingtoinsuf?cientelectronaccumulation.
thusanindicationoftheelectrostaticmodulationofSOIanditsresultingspinsplitting24–29.NotethatwehaveobservedsuchacrossoverfromWLtoWALinanarrowHregime(within±0.5T).Asasignforgate-tunedspin-dependenttransport,theobservedWALpeakbecomesmorepronouncedatlargerns(higherVG),similarlytothosereportedinsemiconductorheterostructures24–29.Totracetherelationshipofnswiththecharacterizedmagnetic
fieldsH??=hˉ/(4el??)andHso=hˉ/(4elso)(wherel??=(Dτ??)1/2isthephasecoherencelength,lso=(Dτso)1/2isthespinrelaxationlengthandDisthediffusionconstant),wehaveanalysedtheobservedmagnetoconductanceusingtwodifferentlocalizationtheoriesbyIordanskii,Lyanda-GellerandPikus30(ILP)andbyMaekawaandFukuyama31(MF).AscanbeseeninFig.3b,amoderatelygoodagreementisfoundbetweentheILPtheoryandourexperimentaldata,especiallyathigh|VG|.AccordingtoFig.3c,HsoincreasesandH??decreasesasnsisincreased,andbothstarttosaturateathighns.ThisindicatestheVGtunabilityofSOIandspinprecession.TheVGdependenceofl??andlsoisshowninFig.3d.l??hasaminimumvalueofabout38nmatns=5.4×1013cm?2andincreasesto140nmatns=6×1014cm?2,implyingthatbyapproachingthemetallicstatetheholesrapidlygainlargerphasecoherence.Ontheotherhand,lsomonotonicallydecreasesasVGincreases,fromabout35nmatns=5.4×1013cm?2to15nmatns=1.9×1015cm?2.Thecrossoverbetweenthel??andlsodirectly
NATUREPHYSICS|VOL9|SEPTEMBER2013|/naturephysics
leadstotheWL–WALtransition.AnalysiswiththeMFtheory(SupplementaryFig.S3)providessimilarinformation.
SuchaWL–WALcrossoverinmagnetoconductancemayseemsimilartothatexpectedinsystemswithgate-tunedRashbaspinsplitting.However,asshowninFig.1e,whenasufficientamountofholesisdopedintoWSe2,theFermipocketsappearnotonlyaroundthe??-pointbutalsoaroundK-points.Consideringthemagnetoconductancedata,thespin-flipimpurityscattering,whichiscrucialfortheWALphenomena,tendstobestrongerforlargermomentaattheBrillouinzonecorners(Kpoints)thanforsmallermomentumatthecentreoftheBrillouinzone(??point)becauseitisproportionalto(k×k??)·σ(detailsaregivenintheSupplementaryInformation).Therefore,theobservedWALisprobablyduetothecontributionofFermipocketsaroundtheK-points,wherethespinsplittingmechanismisnotdescribablebytheRashbaeffect.
Tosupportthisscenario,wehaveperformedopticalreflectionmeasurementsonthebulk-WSe2EDLTdevices.WesummarizethemainresultshereandtheexperimentaldetailsareprovidedintheSupplementaryInformation.Withoutgating,thereisabroadpeakaround2.2eVinthedifferentialreflectionspectrum.Anotherfeaturecanalsobeseenaround1.7eV(althoughitcannotberesolvedproperlyinourmeasurementsowingtoitsweaksignal).Theseopticalfeatures,labelledasBandAexcitons,coincidereasonablywellwiththepreviouslyreportedpeaks32at
(σ (H) ? σ (0))/σ (0)
Δσ (H)/σ0
0.40.30.20.10.0
ns (×1014 cm?2)
lso (nm), lΦ (nm)
ns (×1014 cm?2)
Figure3|SOI-inducedcrossoverfromWLtoWALinWSe2EDLTs.a,Electric?eldmodulationofmagnetoconductance.AclearWL-to-WALcrossoveroccursasnegativeVGincreases.Theverticalarrowslabelled‘0.01’indicatethescaleofrelativeconductance.b,Magnetoconductance??σ/σ0?ttedusingtheILPequation.Here,σ0ise2/h.Experimentalresulblacksolidlinesindicatetheresultoftheoretical?tting.c,Fittingparameters
HsoandH??asafunctionofns.d,Spinrelaxationlengthlsoandphasecoherencelengthl??deducedfromHso,??=hˉ/4elso,??asafunctionofns.Acrossoveroflsoandl??atthelownsregimedirectlycorrespondstothetransitionfromWLtoWAL.Experimentally,lsocanbedirectlymodulatedbychangingtheinterfacialelectric?eldwithliquidgating,indicatingthetuningofspinsplittinginthebandstructure.Errorbarsinc,dcorrespondtotheuncertaintyin?ttingourmagnetoconductancedatatotheILPequation.Bluecurvesinc,dareguidestoeyes.
2.3and1.71eV,respectively.Fromfirst-principlescalculations33,theobservedAandBexcitonshavebeenassignedtotheopticaltransitionsfromtheupperandlowerbranchesofvalencebandstotheconductionbandattheK-point,respectively,asschematicallydepictedinSupplementaryFig.S4c.ByapplyinganegativeVG,boththeAandBexcitonsundergoasignificantchange.FortheBexciton,thischangeappearsasanenergysplittingofthemainpeakintotwosub-peaks.AscanbeseeninSupplementaryFig.S4c,d,theresultingenergysplittingincreasesbyincreasing|VG|.ThisaccordinglysuggeststhatVGenergeticallysplitsthevalencebandsattheK-point(SupplementaryFig.S4c).Aswillbeshownlater,thisobservationisconsistentwithourcalculations,althoughitcannotbeconsideredadirectproof.
Asthe??-pointandK-pointhavedifferentsymmetryproperties,itisimportanttoknowhowtheircorrespondingFermipocketsarespin-polarizedbyVG.Toinvestigatethis,wehaveperformedasetoffirst-principlescalculationsforsufficientlythickslabsofWSe2,exposedtoaperpendicularelectricfieldEex.Figure4a,bshowstherespectivebandstructuresfor6monolayersofWSe2,atEex=0and0.2eV??1(thedetailedevolutionofelectronicstatesunderEexisshowninSupplementaryFig.S5).Asshown,Eexcanindeedinduceahugespinsplittingamongthetopvalencebandswithanenergyorderupto～270meVinthevicinityoftheK-points.Itturnsoutthatthedx2?y2anddxystatesofWaremainlyresponsibleforsuchagiantspinsplitting,asdiscussedindetailinSupplementaryInformation.NotethatSOIcanliftspindegeneracyattheK-point
Hso (T), HΦ (T)
becauseitisnotatime-reversalk-point.Ontheotherhand,nosignificantspinsplittingcanbeseenaroundthe??-point.Wethusruleout(atleasttheoretically)thepossibilityofRashbaspinsplittinginWSe2underEex.Interestingly,theVBM,originallyspin-degeneratedandlocatedatthehigh-symmetry??pointshiftstotheK-pointatsufficientlylargeEexandbecomesfullyspin-polarized.Figure4cshowsthecalculatedFermisurfaceandtheresultingspinpolarizationpatternintheBrillouinzoneoftheWSe2surfaceforEex=0.2eV??1,assumingaFermilevellocated300meVbelowtheVBM.Ascanbeseen,aroundtheKandK??-pointsthespinpolarizationismerelyout-of-planeandZeeman-likebutwithoppositesigns.Thissignchangeisattributedtothefactthatthesek-pointsformaKramersdoublet.AsEexdoesnotbreakthetime-reversalsymmetry,thenthespinpolarizationaroundKhastobeoppositetothataroundK??.Accordingly,thisphenomenondiffersfromaconventionalZeemaneffect,wherethepresenceofmagneticfieldorimpuritiesbreaksthetime-reversalsymmetry.Notethat,assumingareasonableg-factorforWSe2,asignificantlylargeexternalmagneticfield(overseveralhundredTesla)isrequiredtogenerateaZeemanspinsplittingofthesameorder.ThecentralFermipocketaround??remainsspindegenerateevenatEex=0.2eV??1.Thus,theEex-modulatedSOIseemstoselectivelyinducespinsplittingattheK-points.
Thereasonwhythespinsplittingisabsentatthe??-pointwhereasitislargeandout-of-planeattheK-pointcanbeexplainedbythegrouptheory.Asmentionedearlier,eachmonolayerisinvariant
NATUREPHYSICS|VOL9|SEPTEMBER2013|/naturephysics
E ? EVBM (eV)
E ? EVBM (eV)
E = 0.2 eV ??1
Figure4|Effectofexternalelectric?eldonthebandstructuresofWSe2.a,b,BandstructuresofaWSe2slabwithout(a)andwith(b)theexternal
electric?eldEex=0.2eV??1.Blueandredcoloursdenotethebandswithout-of-planespin-upandspin-downpolarizations,respectively.TheVBMisatthe??-pointwithoutEex,whereasitshiftstotheK-pointunderEex.AtunableZeeman-typespinsplittingoccursattheK-point,whereasnosigni?cantspinsplittingcanbeseenaroundthe??-point.c,SpintextureoftheWSe2slabunderEex=0.2eV??1.Here,weassumethattheFermilevelislocated300meVbelowtheVBM(purpledashedlineinb).FermipocketsthatresultedfromZeeman-typespinsplittingcanclearlybeseenattheK-point.The?lledcirclesarespinspointingoutoftheplaneandcircleswithwhitecentresarespinspointinginward.
E = 0.2 eV ?-1
Energy (eV)
Energy (eV)
E = 0.2 eV ?-1
Energy (eV)
Energy (eV)
Bottom WSe2
WSe2 bilayer
Figure5|Originofout-of-planespinpolarizationinWSe2undertheexternalelectric?eld.a,b,ElectronicbandstructuresofamonolayerofWSe2under
aperpendicularelectric?eldEex=0(a)and0.2eV??1(b).Blueandreddotsrepresentspin-upandspin-down.Owingtothepresenceofthein-planeelectricdipolemoment,themonolayer’sbandstructureshowsout-of-planespinpolarization,irrespectiveoftheapplicationofEex.c,d,ElectronicbandstructuresofabilayerofWSe2underEex=0(c)and0.2eV??1(d).Cancellationofthein-planeelectricdipoleleadstotheabsenceoftheout-of-planespinpolarizationinbilayerWSe2.However,theapplicationofaperpendicularEexbreaksspatialinversionsymmetryandthusallowseachmonolayertopartiallyretainitsin-planedipolemomentleadingtoanout-of-planespinpolarizationtunablebyEex.e,Schematicsofelectric-?eldeffectonthebandstructureofbilayerWSe2.LightblueandlightredshadingcorrespondstotheelectronicstructuresintheabsenceandpresenceofEex,respectively.
NATUREPHYSICS|VOL9|SEPTEMBER2013|/naturephysics
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