Deformation of the Fermi surface in the extended Hubbard mod

The deformation of the Fermi surface induced by Coulomb interactions is investigated in the t-t'-Hubbard model. The interplay of the local U and extended V interactions is analyzed. It is found that exchange interactions V enhance small anisotropies produc

DeformationoftheFermisurfaceintheextendedHubbardmodel

UnidadAsociadaICMM-UC3M,InstitutodeCienciadeMateriales,ConsejoSuperiordeInvestigacionesCient´ cas.

Cantoblanco,28049Madrid.Spain.

2UnidadAsociadaICMM-UC3M,DepartamentodeMatem´aticas,UniversidadCarlosIIIdeMadrid,Avda.delaUniversidad

30,28911Legan´es,Madrid,Spain.

(February1,2008)1B.Valenzuela1andM.A.H.Vozmediano2

arXiv:cond-mat/0007135v1 [cond-mat.str-el] 7 Jul 2000ThedeformationoftheFermisurfaceinducedbyCoulombinteractionsisinvestigatedinthet t′–Hubbardmodel.TheinterplayofthelocalUandextendedVinteractionsisanalyzed.ItisfoundthatexchangeinteractionsVenhancesmallanisotropiesproducingdeformationsoftheFermisurfacewhichbreakthepointgroupsymmetryofthesquarelatticeattheVanHove lling.ThisPomeranchuckinstabilitycompeteswithferromagnetismandissuppressedatacriticalvalueU(V).TheinteractionVrenormalizesthet′parametertosmallervalueswhatfavorsnesting.ItalsoinduceschangesonthetopologyofholeoftheFermisurfacewhichcangofromholetoelectron-likewhatmayexplainrecentARPESexperiments.71.10.Fd,71.10.-w,74.20.MnTheshapeoftheFermisurfaceplaysacrucialroleindeterminingtheinstabilitiesofinteractingFermisystems.TheimportanceofFermisurfacedeformationsbyinteractioninthenon-sphericalcasewasalreadyrecognizedintheearlypapersonthefoundationoftheFermiliquidconcept[1,2],andremainsacentralquestionbothunderafundamentalpointofviewaswellasforthephenomenologicalimplications.ThephysicsofthecupratesandtherecentARPESexperimentshasrenewedinterestontheanisotropicFermisurfaces.MainquestionsarehowcloseisthemeassuredFermisurfacefromthenon–interacting?,howmuchcantheFermisurfacebedeformedbeforeitbreaksdowndrivingthesystemtoabrokensymmetryphase?,doesthedeformationalwaysrespectthepointgroupsymmetryofthelattice?Inthispaperweaddresstheformerquestionsinaverysimpli edmodelofthecuprates.WestudytheFermisurfacedeformationinthet t′–Hubbardmodelonthesquaredtwo–dimensionallatticeinthepresenceofweektomoderateCoulombinteractions.Weincludeanon-sitecouplingUtotakeaccountofthemagneticinteractionsandanextendedexchangeinteractionVwhichcanbeaslargeast[3]andiswidelyusedrecentlytoaccountforthestripefeatureandthepossiblephaseseparatedphaseinthecuprates.ItwillbeseenthattheVinteractionplaysacrucialrolewhentheshapeoftheFermisurfacedoesnothavespecialfeaturesfavoringmagneticinstabilities.ThedeformationoftheFermisurfaceintheHubbardandt Jmodelshasbeenstudiedrecently[4–7]withavarietyofmethods.Inmostoftheseapproachesattentioniscenteredonthein uenceofmagneticinteractionssotheexchangeinteractionVisnottakenintoaccount.Ourresultsshowthat,evenatthemean eldlevel,thisinteractionhasastrongin uenceontheFermisurfacerenormalization.InaveryrecentpaperitwasarguedthattheFermisurfaceofthet t′–Hubbardmodelmayundergoadeforma-tionbreakingthepointsymmetryoftheunderlyinglattice(Pomeranchuckinstability)drivenbytherenormalizationoftheforwardchannel.AdeformationofthistypeseemstobeobservedinrecentARPESexperimentsFerromag-neticinstabilitieswhichwoulddirectlycompetewiththePomeranchuckinstabilitywerenottakenintoaccount.WeinvestigatetheconditionsfortheformationofPomeranchuckinstabilitiesandthecompetitionwithferromagnetism.Wearguethattheinstabilityisa netuninge ectwhichonlytakesplaceattheVanHove llingandissuppressedbyferromagnetism.

Ouranalysisprovidesalsointerestingresultsconcerningtherenormalizationofthet′parameterwhichisshowntodecreasewithV.

Thehamiltonianthatweshalluseis

+ni,↑ni,↓+Vnisnjs′,(1)tijci,σcj,σ+UH=

i,j,σi<ij>,ss′

wheretij=tfornearestneighbors,tij=t′fornextnearestneighbors,anditiszerootherwise,andwherewehaveincludedanextendedCoulombinteractionV.

Thenon-interactingbandstructureof(1)inthesquaredlatticeis

1

The deformation of the Fermi surface induced by Coulomb interactions is investigated in the t-t'-Hubbard model. The interplay of the local U and extended V interactions is analyzed. It is found that exchange interactions V enhance small anisotropies produc

ε0(k)= 2tcoskx 2tcosky+4t′coskxcosky

whatoriginatestheconstantenergycontoursshownin g.1.(2)

3

2

1

0-1-2

-3

FIG.1.Fermisurfaceofthefreesystemfort=1,t’=0.3andvariousdensitiesaroundtheVanHove lling.

TheshapeoftheinteractingFermisurfaceisencodedinthetwo–pointGreen’sfunctionoftheinteractingsystem

G(ω,k)=1

The deformation of the Fermi surface induced by Coulomb interactions is investigated in the t-t'-Hubbard model. The interplay of the local U and extended V interactions is analyzed. It is found that exchange interactions V enhance small anisotropies produc

hasbeencomputedintheliterature[4,7]andfoundtobeverysmall.TheinteractionVcontributestothefermionself–energyattheonelooplevelthroughdiagramin g.2b).

Wecomputenumericallythecontributionofdiagramin g.2b)totheFermisurfacedeformationineq.(4)bysolvingself-consistentlytheequation

ε(k)=εkin(k)+εexch(k) µ

= 2tcoskx 2tcosky+4t′coskxcosky 2V

′,k′kxy′′[cos(kx kx)+cos(ky ky)]n(k′) µ,(6)

whereµisadjustedsothatthetotalnumberofelectronsremainsconstantandspininteractionsarenottakenintoaccount.

Ferromagnetismisincludedbystartingwithtwodi erentFermisurfacesforelectronswithspinupanddownandsolvingtheequations

n↓exch(k)+ε(k)+Uε↑(k)=ε0↑↑

µ,(7)N

wherethetotalnumberofelectronsN=n↑+n↓remainsconstant.

Fromeqs.(6)and(7),itisclearthatintheabsenceofferomagnetism,i.estartingwithtwoidenticalFermisurfacesin(7),theinteractionUcontributestothetotalenergywithaglobalconstantthatisabsorbedinthechemicalpotential.ThedeformationsinducedbyVareingeneralsimilartotheonesobtainedintheliteratu …… 此处隐藏：5859字，全部文档内容请下载后查看。喜欢就下载吧 ……