The Fermi surface of Bi2Sr2CaCu2O8(2)

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