The Fermi surface of Bi2Sr2CaCu2O8

We study the Fermi surface of Bi2Sr2CaCu2O8 (Bi2212) using angle resolved photoemission (ARPES) with a momentum resolution of ~ 0.01 of the Brillouin zone. We show that, contrary to recent suggestions, the Fermi surface is a large hole barrel centered at (

TheFermisurfaceofBi2Sr2CaCu2O8

H.M.Fretwell,1 A.Kaminski,1,2J.Mesot,2 J.C.Campuzano,1,2M.R.Norman,2M.Randeria,3T.Sato,4R.

Gatt,1T.Takahashi,4andK.Kadowaki5

arXiv:cond-mat/9910221v1 [cond-mat.supr-con] 14 Oct 1999

(1)DepartmentofPhysics,UniversityofIllinoisatChicago,Chicago,IL60607(2)MaterialsSciencesDivision,ArgonneNationalLaboratory,Argonne,IL60439

(3)TataInstituteofFundamentalResearch,Mumbai400005,India(4)DepartmentofPhysics,TohokuUniversity,980-8578Sendai,Japan(5)InstituteofMaterialsScience,UniversityofTsukuba,Ibaraki305,Japan

WestudytheFermisurfaceofBi2Sr2CaCu2O8(Bi2212)usingangleresolvedphotoemission(ARPES)withamomentumresolutionof～0.01oftheBrillouinzone.Weshowthat,contrarytorecentsuggestions,theFermisurfaceisalargeholebarrelcenteredat(π,π),independentoftheincidentphotonenergy.PACSnumbers:71.25.Hc,74.25.Jb,74.72.Hs,79.60.Bm

TheFermisurface,thelocusinmomentumspaceofgaplesselectronicexcitations,isacentralconceptinthetheoryofmetals.Despitethefactthattheopti-mallydopedhightemperaturesuperconductorsdisplayananomalousnormalstatewithnowell-de nedquasi-particles[1],manyangleresolvedphotoemissionspec-troscopy(ARPES)studiesusingphotonenergiesintherangeof19-22eVhaveconsistentlyrevealedalargehole-likeFermisurfacecenteredat(π,π)[2–5]withavolumeconsistentwiththeLuttingercountof(1 x)electrons(wherexistheholedoping).Thiswidelyacceptedpic-turehasrecentlybeenchallengedbytwostudies[6,7]whichsuggestadi erentFermisurfacewhenmeasuredatahigherphotonenergy(32-33eV).Theserecentstud-iesproposethattheFermisurfaceconsistsofalargeelec-tronpocketcenteredon(0,0)withaclearviolationoftheLuttingercount.Toreconciletheirmodelwithpreviousdataat22eVphotonenergy,theseauthorssuggestthepresenceof“additionalstates”near(π,0),possiblyduetostripeformation.SettingasideforthemomenttheimportantquestionofwhatthetrueFermisurfaceofBi2212is,theimplicationofaphotonenergydependentFermisurfacefromARPESdataisparticularlyworri-some,anddeservestobeaddressed.

Here,wepresentextensiveARPESdatatakenatvar-iousphotonenergiesand ndclearevidencethattheFermisurfacemeasuredbyARPESisindependentofphotonenergy,andconsistsofasingleholebarrelcen-teredat(π,π).AlthoughthedataofRefs.arecon-sistentwithours,theirlimitedsamplingoftheBrillouinzoneandlowermomentumresolutionleadtoamisin-terpretationofthetopologyoftheFermisurface.ThisoccursbecauseofthepresenceofghostimagesoftheFermisurfaceduetodi ractionoftheoutgoingphoto-electronsbyaQvectorof±(0.21π,0.21π)associatedwiththesuperlatticemodulationintheBiOlayers(umklappbands).Inparticular,infollowingaFermicontour,ifthedataarenotdenseenoughink-space,ornotofsu -cientlyhighmomentumresolution,onecaninadvertently“jump”fromthemainbandtooneoftheumklappbands,concludingincorrectlythatthetopologyoftheFermisurfaceiselectron-like.Thisisparticularlyrelevantatthephotonenergyof33eVbecauseofastrongsuppres-sionoftheARPESmatrixelementsatkpointsinthevicinityof(π,0),a nalstatee ect,resultinginalargeumklapp/mainbandsignalrationear(0.8π,0)wherethepurportedelectronFermisurfacecrossingoccurs.

ARPESprobestheoccupiedpartoftheelectronspec-trum,andforquasi-2DsystemsitsintensityI(k,ω)isproportionaltothesquareofthedipolematrixelement,theFermifunctionf(ω),andtheone-electronspectralfunctionA(k,ω)[8].Themeasuredenergydistributioncurve(EDC)isobtainedbytheconvolutionofthisinten-sitywithexperimentalresolution.Inanotherpaper,wediscussingreatdetailthevariousmethodologiesforde-terminingtheFermisurfacefromARPESdataHere,welookattwoquantities:(1)thedispersionofspectralpeaksobtainedfromtheenergydistributioncurves,and(2)theARPESintensityintegratedoveranarrowenergyrangeabouttheFermienergyAswewillshow,thesemethodsmustbetreatedwithcarebecauseofthekde-pendenceofthematrixelementsandthepresenceoftheumklappbands.

TheARPESexperimentswereperformedattheSyn-chrotronRadiationCenter,Wisconsin,usingaplanegratingmonochromatorbeamlinewitharesolvingpowerof104at1012photons/s,combinedwithaSCIENTA-200electronanalyserusedinangleresolvedmode.Atypicalmeasurementinvolvedthesimultaneouscollec-tionandenergy/momentumdiscriminationofelectronsovera～12 range(cut)withanangularresolutionwin-dowof～(0.5 ,0.26 )(0.26 paralleltothecut).Thiscorrespondstoamomentumresolutionof(0.038,0.020)π,(0.029,0.015)π,and(0.022,0.012)πat55,33,and22eVrespectively.Theenergyresolutionforalldatawas～16meV(FWHM).

Thequalityoftheoptimallydopedsinglecrystalsam-plescannotbeemphasizedenough,particularlyinre-

We study the Fermi surface of Bi2Sr2CaCu2O8 (Bi2212) using angle resolved photoemission (ARPES) with a momentum resolution of ~ 0.01 of the Brillouin zone. We show that, contrary to recent suggestions, the Fermi surface is a large hole barrel centered at (

FIG.1.(a)IntensityI(k,ω)and(b)EDCsalongΓYmea-suredonanoptimallydopedsample(Tc=90K)atT=40Kwith33eVphotonspolarizedalongΓX.Main,umklapp,sec-ondorderumklapp,andshadowbandsaredenotedasMB,UB,UB(2),andSB.(c)Integratedintensity(-100to+100meV)coveringtheXandYquadrantsoftheBrillouinzone.Datawerecollectedonaregularlatticeofkpoints(spac-ing1 alongΓXand0.26 alongΓY).Overlaidon(c)isthemainband(black),±umklapps(blue/red),and±2ndorderumklapps

(dashedblue/redlines)Fermisurfacesfromatightbinding t[13].

gardstothe atnessofthesurfaceaftercleave.Achangeof1µminheightoverthewidthofthesampleisreadilydetectableasabroadeningofthespectralfeatures,andthereforecarewasexercisedinstudyingvery atsampleswithsharpx-raydi ractionrockingcurves.ReferencespectrawerecollectedfrompolycrystallineAu(inelec-tricalcontactwiththesample)andusedtodeterminethechemicalpotential(zerobindingenergy).

Tobeginwelookatdata,Fig.1,takenonanoptimallydopedBi2212sample(Tc=90K),measuredatT=40K[10]at33eV.ThelightpolarizationwasparalleltoΓX(weusethenotationΓ=(0,0),X=(π, π),Y=(π,π)andM=(π,0),withΓYparalleltothesuperlatticemodula-tion)andEDCswerecollectedonaregularlatticeofkpoints(δkx=1 ,δky=0.26 ).We rstexaminespec-traalongtheΓYdirection.TheEDCsareshowninthemiddlepanelofFig.1,andtheleftpanelshowsatwodi-mensionalplotoftheenergyandmomentumdistributionofthephotoelectronsalongtheΓYcut.Astrongmainband(MB)andadditionalumklappbands(UB)canbeobservedinthisplot.Around(0,0),thereisaweakerpairofhigherorderumklapps(UB(2)correspondingtoatranslationof±(0.42,0.42)π)asobservedpreviously[11],whichcon rmsthedi ractionoriginoftheumklappbands.Alongthiscut,wealsoseethe(π,π)translation

FIG.2.(a)TightbindingFermisurfacefromRef.[13]anditsumklappimages.(b)Integratedintensity(-100to+100meV)fromfourquadrantsoftheBrilliounzone.Datameasuredusing33eVphotonsonanoptimallydopedsample(Tc=90K)atT=40KwiththesamekpointspacingasFig.1.LightpolarizationisalongΓM.DashedportionsontheFermisurfaceoverlayfrom(a)indicateintensitysuppresionduetomatrixelements.Notethatbecauseoftheumklapps,thisleadstoadiagonal-likesuppressionoftheintensityaroundM.(c)SlicesparalleltoMYfrom(b)inanexpandedregionaboutM(thickblacklineistheMYslice).(d)Dataarti ciallybroadenedinkresolutionbyinterpolating(c)ontoanewklattice(spacing2 ).ReddashedlinesindicatetheFermisurfacecontourssuggestedinRefs.[6,7].

ofthemainband,theso-calledshadowband(SB)[4],whichisprobably[5]associatedwiththetwoformulaunitsperbaseorthorhombicunitcell.Fig.1cshowstheintegratedintensitywithina±100meVwindowaboutthechemicalpotential.Wenotetheveryrapidsuppres-sionofintensitybeyond～0.8ΓM[12],whichdoesnotoccurat22eV.ThisiswhatledtheauthorsofRefs.[6,7]tosuggesttheexistenceofanelectron-likeFermisurfacewithacrossingatthispoint.As rstdiscussedinanearlierpaper[5],andaddressedingreaterdetailhere,wewilldemonstratethatinstead,thiscrossingisduetooneoftheumklappbands.Thisumklappcrossingismoreobviousat33eV,since,unlikeat22eV,themainbandintensityissuppressedbymatrixelemente ects[9].Toexaminethisissuemoreclosely,wemeasuredan-otheroptimallydopedsample(Tc=90K,T=40K)with33eVphotonspolarizedparalleltoΓM,showninFig.2,withthesamehighdensityofk-pointsasfortheΓXori-entedsample.TheintegratedintensityatEFissimilartotheΓXorientedsampleinthatthereisan‘apparent’closedFermisurfacearound(0,0),indicatedbyanarrow

We study the Fermi surface of Bi2Sr2CaCu2O8 (Bi2212) using angle resolved photoemission (ARPES) with a momentum resolution of ~ 0.01 of the Brillouin zone. We show that, contrary to recent suggestions, the Fermi surface is a large hole barrel centered at (

inFig.2b.However,oncloserinspectionofthe(π,0)re-gion,weseewhatistrulyoccuring.Fig.2cshowsslicesparalleltoMYfromtheplotofFig.2b.Themainband(MB),indicatedbytheshortblackbars,continuestorunparalleltoΓM,butitsintensityisheavilysuppressednearM.Inaddition,the(+)umklappband,indicatedbyredbars,splitsawayfromthemainband,dispersestowardsM,anddiesinintensity.Atransposedversionofthisoc-cursbeyondMwiththe( )umklapp,indicatedinblue.SimilarbehaviourisalsoseenattheMpointatthetopofFig.2b(slicesnotshown)andintheΓXorientedsampleofFig.1c.

ItiseasytoseehowsparsedataatlowerresolutioncaneasilyleadonetomissthesuppressedmainbandcrossingalongMYat33eV.Fig.2dshowsaplotsimilartotheoneinFig.2c,butata

resolutionof(0.11,0.11)π-thesameasthatusedinRef.[7]-insteadof(0.029,0.015)πinFig.2c.Clearly,itisnolongerpossibletodistinguishtheumklappfromthemainband(MB),andonemightwronglysupposethattheFermisurfacecurvesaroundtocrosstheΓMline.Butweemphasizeagainthatsuchasuppositionisonlyaresultofsparsedata,andnotofanyinherentdi erencesinexperimentalresults.ItisworthnotingthatintheΓXorientedsample(Fig.1c)wecanseeaweaksignalcorrespondingtothemainbandMYFermicrossing,whichbecomesstrongerat22eV.Therefore,ifquantitiesbasedonintegratedintensityareusedtode netheFermisurface,onemayfalselyinferacrossingalongΓMduetothe(+)umklappband,asindicatedinFig.2d.Thepresenceoftheumklappscanalsoexplaintheori-ginoftheasymmetryintheunderlyingintensityplotatMinFig.2b.At33eVtheARPESsignalfromthemainbandisstronglysuppressednearMduetothema-trixelements,butsincetheumklappsaretranslatedby±(0.21,0.21)π,wegetadiagonal-likesuppressionofthetotalsignalnearM.ThiscanbeappreciatedbylookingatthedashedsegmentsoftheoverlayonFig.2b.Thatis,theumklappsignalatkiscomparableinintensitytothemainbandsignalatk±Q,asexpectediftheumklappissimplyadi ractionoftheoutgoingphotoelectronsbytheBiOsuperlattice.

Accordingtothispicture,whenmovingalongΓM,thereshouldbeacrossoverfromthe(+)to( )umk-lapp,andthisisinfactseenintherawdata.Fig.3showextensiveEDCstakenincutsparalleltoMYatk-pointsalongΓMfor33eV.Inmostoftheseplots,themainband(crossingshownbyablacksquare)isthestrongestsignalandthe±umklapps(crossingsshownasblackandwhitearrows)areaweakersignalsuperimposedneartheΓMline.Aconstanto sethasbeenusedinthe guressothattheumklappcrossingsappearasa“bunching”ofthespectra.GoingfromΓtoMwesee,inthefollowingorder,the( )umklapp(whitearrow),the(+)umklapp(blackarrow)whichdisappearsat(π,0),and nallythereappearanceofthe( )umklapp(whitearrow).We ndthatthedispersionofallthemainandumklappsignals

FIG.4.(a)NearEFintensity(integratedover±100meV)at55eVfortheΓXorientedsampleofFig.1mea-suredatT=40K.NotethestrikingsimilaritytothelargeholeFermisurface(solidcurves)withitsumklappimages(dashedcurves)shownin(b).

areconsistentwiththetightbinding ttothedispersionat19-22eV[13,5].Thedi erenceisthatat22eV[5],thesuppressionofthesignalat(π,0)isweaker,andtheMYcrossingofthemainbandisclearer.

InFig.4a,weshowanintensitymapfromthesampleofFig.1,butat55eVphotonenergy.Fromthisintensityplot,onecanclearlyseethemainFermisurfaceanditstwoumklappimages,andthecorrelationofthisimagewithasinglelargeholesurfacearound(π,π)togetherwithitspredictedumklappimages(Fig.4b)isstriking.Inconclusion,we ndthattheFermisurfaceofBi2212isasingleholebarrelcenteredat(π,π),aresultwhichwe ndtobeindependentofphotonenergy.Rather,wehavedemonstratedthattheunusualintensityvariationobservedbypreviousauthorsat33eViscausedbyacombinationofmatrixelemente ectsandthepresenceofumklappbandscausedbythedi ractionofthepho-toelectronsfromtheBiOsuperlattice.

ThisworkwassupportedbytheUSNationalScienceFoundation,grantsDMR9624048,andDMR91-20000throughtheNSFScienceandTechnologyCenterforSu-perconductivity,theUSDeptofEnergyBasicEnergySciences,undercontractW-31-109-ENG-38,theCRESTofJST,andtheMinistryofEducation,ScienceandCul-tureofJapan.TheSynchrotronRadiationCenterissup-portedbytheNSFgrantDMR-9212658.M.R.wassup-portedinpartbytheIndianDSTthroughtheSwarna-jayantischeme.

We study the Fermi surface of Bi2Sr2CaCu2O8 (Bi2212) using angle resolved photoemission (ARPES) with a momentum resolution of ~ 0.01 of the Brillouin zone. We show that, contrary to recent suggestions, the Fermi surface is a large hole barrel centered at (

FIG.3.EDCsforcutsparalleltoMY(seeinset)measuredatT=40Kfor33eVphotonenergy.Notechangeinbindingenergyaxisscaletoemphasizequasiparticledispersion.SamesampleandorientationasFig.2.Theblacksquaresindicatethemainbandcrossings,andtheblackandwhitearrowstheumklappbandcrossings.ThezoneinsetisasinFig.2a,withdashedsegmentsontheFermicontoursindicatingmatrixelementsuppression,andtheverticallinesrepresentingthecuts.

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