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MagneticGapofFe-dopedBiSbTe2SeBulkSingleCrystalDetectedbyTunnelingSpectroscopyandGate-controlledTransports:SupportingInformationRikizoYano,,y,z,@AndreiKudriashov,{HishiroT.Hirose,xTaikiTsuda,zHiromiKashiwaya,kTakaoSasagawa,xAlexanderA.Golubov,{,?VasilyS.Stolyarov,,{,#,@andSatoshiKashiwaya,zyIMaSS,NagoyaUniversity,Nagoya464-8603,JapanzAppliedPhysics,NagoyaUniversity,Nagoya464-8603,Japan{TQPSSLab,CenterforPhotonicsand2DMaterials,MoscowInstituteofPhysicsandTechnology,Dolgoprudny,141700Moscow,RussiaxLaboratoryforMaterialsandStructures,TokyoInstituteofTechnology,Yokohama226-8503,JapankNationalInstituteofAdvancedIndustrialScienceandTechnology(AIST),Tsukuba305-8568,Japan?FacultyofScienceandTechnologyandMESA+InstituteofNanotechnology,7500AEEnschede,TheNetherlands#DukhovResearchInstituteofAutomatics(VNIIA),127055Moscow,Russia@RYandVScontributedequallytothiswork.E-mail:yano-rikizo@nagoya-u.jp;vasiliy.stoliarov@gmail.com;s.kashiwaya@nagoya-u.jp1
1S1:SamplepreparationandcharacterizationSinglecrystalsofFe-BSTSweregrownusingmodi edBridgmanmethodbasedonFe/Mn-dopedBiSe,S1Fe-dopedBiTeSe,S2andFe-BSTS.S3High-puritystartingmaterials(Fe:Bi:Sb:Te:Se2322=0.1:0.95:0.95:2:1)wereloadedintoanevacuatedquartztubewithasharp-pointedbottom.Beforestartingcrystalgrowth,themeltedsamplewasrepeatedlyphysicallyshakenabovethemeltingtemperaturetoachievecompletelyhomogeneousmelting,asdescribedbyY.L.Chenetal.,S1,S3followedbyrapidwaterquenching.Thealloywasrapidlyheatedandslowlycooledfromthebottomside,wherethecrystallizationstarted,inatemperature-gradientfurnace.Afterthecrystallizationprocess,rapidwater-quenchingfromahightemperature(above500oC,higherthantheprevioustemperatureS3)wasalsoperformedtopreventseg-regationintootherFe{Secompounds.Thisprocessandquenchingtemperaturearecriticalforobtainingmagneticimpurity-free,sizablecrystals.FigureS1:Samplecharacterization.(a)XRDpatternsofcleavedplanesofFe-BSTSsinglecrystal.Theloweroneisasimulatedpatternfromthe(00`)planes.Theinsetshowstypicalgrowncrystals.(b)HomogeneousspatialdistributionofchemicalcompositionsinacleavedrectangularFe-BSTScrystalbySEM-EDX.ThebottompanelindicatestheintergrowthofFe{SecompoundsinFe-dopedBi2Te2Seasabadexample.ThebulkcrystalsofFe-dopedBiSbTe2Sewereeasily,mechanicallycleavedintolargecrystalplatesusingaknifeandtape(insetinFig.S1(a)).XRDmeasurementswereobtainedatroomtemperatureusingaCuK inD2PHASERpowderdi ractometerwithLynxExe2
21Ddetector(Bruker).Thecleavedplaneswere(00`)planes,showingasharppeakonlyat003mintheXRDpattern(Fig.S1(a)).Thelatticeparameterofthec-axiswas29.97A,consistentwiththepreviousreport,S3andslightlysmallerthan30.04Aofnon-dopedBiSbTeSe.S4ThisshiftensuressubstitutionwiththesmalleratomsofFefor(Bi,Sb)sites.2Wecarefullycon rmedtheabsenceofimpurityphasessuchasFe{SecompoundsdescribedinrefS5,byrepeatedlycleavingoneplatecrystalandcheckingtheXRDpatterns.SpatialchemicaldistributionanalysiswasperformedusinganEDXanalyticalsystemequippedwithanSEM(Quanta200FEG:FEI).TheEDXanalysisindicatedahomogeneouschemicaldistribution(Fig.S1(b)upper).Despitedarknesssignals,wecon rmedtheFe-concentrationabovebackgroundnoiselevels.WhenweinvestigatedFe-dopedBi2Te2Segrownundernon-optimumconditions,EDXdetectedtheintergrowthofFe{Secompounds(lowerpanelsofFig.S1(b)).ThisindicatesthatthespatialdistributionofSeismoresensitivetotheintergrowthoftheFe{Secompounds,andthehomogeneousSedistributionofFe-BSTSensuresnoremarkableFe{Seimpurity.ThechemicalcompositionofFewasapproximately0.01,comparabletotheestimatedvaluefromthelatticeshrinkingusingtheionicradiiofFe3+(0.645A)andanaveragedBi3+{Sb3+(0.895A)withsix(Bi,Sb)sitesinoneunitcellalongthec-axis.3
3S2:FabricatingEDLTdeviceusingabulkcrystalFigureS2:Devicefabricationprocess.(a)BondingAu-wires(b)Coveringthecrystalbyepoxyresin.(c)MakinganIL-gate(d)Schematicmanufactureddevicewithexternalmeasurementcircuitwiththreelabels:(left)No-IL,(middle)w/ogating,and(right)gatedlabels.(e)TopviewoftheNo-ILsetup(d)andopticalphotograph.Fig.S2showstheexperimentalcon guration.First,wefabricatedAupadsonabulkcrystalplatebyAu-sputtering.Then,webondAuwirestothesampleusingAgpaste(a).AftertheAgpastedriedoutcompletely,theepoxyresincoveredthecrystaledgeandonlyallAgpastetoprotecttheAgpastefromtheelectrochemicalreactionwiththeIL.TheAupadswereneverwhollyenclosedbytheresintocontacttheIL.Inthelaststep,wemadeatop-gatewithaAuplateandinsertedtheIL(DEME-TFSI).Allvoltagecontrollingoccurredat230KinthevacuumedPPMS.Whenapplyingthegatevoltage,wecarefullywatchedtheleakcurrenttopreventchemicalreactions.Becausethemeasurementcurrentmaya ectthecarrierdensities,weperformedalltransportmeasurementsaftercoolingbelowtheglass-transition(freezing)temperatureoftheIL.Wecheckedthevalidityofthiscon gurationbyinvestigatinggated2H-MoS2resultingfromthesamesuperconductingnature,includingthecarrier-criticaltemperaturephasediagraminRefS6.4
4IntheMRdata,wecorrectedthemixedcontributionofthelongitudinalresistanceRxxandHallresistanceRxybyreversingthemagnetic elddirectionasRxx=(Vxx(H)+Vxx( H))=2IandRxy=(Vxy(H) Vxy( H))=2I=RHall.Wecalculated3Dlongitudinalconductivityfrom==(2+2).xxxxxxxxxy5
5S3:DetailmagnetotransportpropertiesFigureS3:Magnetotransportpropertiesofas-growncrystals(No-IL).(a)Mag-netic elddependenceoftheresistivityoftheas-growncrystalatvarioustemperatures.Theblackdashedlineisthecalculatedresistivityxxusingthetwo-bandmodelwiththeoptimumparametersfromtheHallresistivityHallat2K.(b)AngulardependenceofthemagnetoresistanceoftheNo-ILcrystalwithamagnetic eldof8Tatvarioustempera-tures.(c)TemperaturedependenceofHallresistivityatvarioustemperaturesrangingfrom2to100K.Thesolidblacklinesindicatethe ttingresultsusingthetwo-bandmodel.(d)Magnetoresistancewithaperpendicularmagnetic eldat2K.FigureS3(a)showstheresistivityunderperpendicularmagnetic eldsatvarioustemper-atures.Theresistivityrapidlyincreasedbyapplying elds,showingcusp-shapedbehaviorsthatwerremaintainedupto50K.Thedashedlinesshowtheconventional eld-dependence6
6calculatedusingthetwo-bandmodel:(2+2)+(R2+R2)B2(B)=surfbulkbulksurfsurfbulkbulksurf:xx(+)2+(R+R)2B2surfbulksurfbulkWeusedtheparametersfromtheobtained ttingresultoftheHallresistivityxy(B)(seedetailsinthemaintext).Thediscrepancybetweenthedataandthecalculatedxxcomesfromanadditionalcontributionfromthe2Dweakantilocalizatione ect.ThevalueofMR;=((H) (0))=(0),reached100%at2K.AngulardependenceofMRat8Tshowedasimplejcosjdependence,indicatingthatthe2Delectronnaturecomesfromsurfacestates(Fig.S3(b)).FigureS3(c)showsthetemperatureevolutionoftheHallresistivity.Whilethehigh-temperaturelinesshowalmostlinear eld-dependence,thelow-temperaturelinesshowagentlecurve,indicatingatleastatwo-carriercontribution.Weobtainedanexcellent ttingresultusingthetwo-bandmodelshownbythesolidline.Figure3(d)inthemaintextillustratestheobtainedparameters.ThevalueoftheMRchangedwithin70%-110%byapplyinggatevoltages(Fig.S4(d)).No-ILshowedthehighestvalue,re
ectingtheFermienergypositionclosesttotheDP.References(S1)Chen,Y.;Chu,J.-H.;Analytis,J.;Liu,Z.;Igarashi,K.;Kuo,H.-H.;Qi,X.;Mo,S.-K.;Moore,R.;Lu,D.etal.MassiveDiracFermionontheSurfaceofaMagneticallyDopedTopologicalInsulator.Science2010,329,659{662.(S2)Yano,R.;Koyanagi,M.;Kashiwaya,H.;Tsumura,K.;Hirose,H.T.;Asano,Y.;Sasagawa,T.;Kashiwaya,S.UnusualSuperconductingProximityE ectinMagneti-callyDopedTopologicalJosephsonJunctions.J.Phys.Soc.Jpn.2020,89,034702.(S3)Yano,R.;Hirose,H.T.;Tsumura,K.;Yamamoto,S.;Koyanagi,M.;Kanou,M.;Kashi-waya,H.;Sasagawa,T.;Kashiwaya,S.Proximity-InducedSuperconductingStatesof7
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