The Fermi surface of Bi2Sr2CaCu2O8(3)

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.