Deformation of the Fermi surface in the extended Hubbard mod(2)

WehavesearchedforPomeranchuckinstabilitiesbyinvestigatingtheresponseofthesystemtoverysmallper-turbationsofthefreeFermisurface.Theresultisextremelysensitivetothevalueofthechemicalpotentialofthe nalsystem.Thee ectoftheinteractionsis,ingeneral,torestorethelatticesymmetryforgenericvaluesofthe nalµ.Eveninthecaseofverystronginitialperturbation(oftheorderofa4percent),the nalFermisurfaceisfour-foldsymmetric.TheexceptionariseswhenthechemicalpotentialoftheinteractingsystemcoincideswiththeVanHovesingularity.Wehavecheckedthat,intheabsenceofferromagnetism,theVanHove llingisunstabletowardsPomeranchuckdeformations.Thisresultagreeswiththegeneralconsiderationsexposedin[14]thattheFermilevelofelectronsystemstendtoavoidpeaksinthedensityofstates.

Fig.3showsthedeformationcausedbyV=2inaparamagneticsituationwhenapointisremovedbyhandintheinitialFermisurfaceofa61x61lattice(correspondingtoananisotropyoflessthan10 3).

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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

FIG.3.DeformationoftheFermisurfaceinducedbyVandbyasmallanisotropyinthefreeband.Solidline:freeFS;dottedline: nalFSintheabsenceofanisotropies;dashedline:deformedFS.

ThesolidlinerepresentsthefreeFermisurface,thedottedlineistheinteractingFermisurfaceintheabsenceoftheperturbation,andthedashedlineshowsthe nalFermisurfaceobtainedafterperturbingthefreeFermisurface.Similarresultsareobtainedwithdi erentvaluesofV(n).Thisresultisindependentoft′andoccursalsoatt′=0.Itisneverthelessextremelysensitivetothevalueofthe nalchemicalpotentialwhichhastobe netunedbyselectingtheinitialnumberofparticles.

Magneticinteractionsdosubstantiallychangetheformerpicture.Wehave

centeredourattentiononthee ectofferromagnetismasthepredominantcompetinginteractionintheforwardchannel[16].OurresultsshowthatferromagnetismisenhancedbyUandt′asexpected,butitisdisfavoredbyV.ThiscanbeunderstoodonthelightofourpreviousanalysisshowingthatVrenormalizesthet′parameterdownwards.ForsmalltomoderatevaluesofU,thefreeferromagneticsystemevolvestoaninteractingparamagneticstate.Thereis,however,acriticalvalueofU(V)wherethe nalstatecorrespondstoafullypolarizedferromagneticsystem.Thissupressionofferromagnetismbyexchangeinteractionsmightexplaintheabsenceofferromagneticphasesinrealsystemswhichareotherwisewelldescribedbythet t′–Hubbardmodelastheonein[16].

ThePomeranchuckinstabilitiesdescribedabovecompetewithferromagnetism.AschematicphasediagramshowingtheevolutionoftheferromagneticbehaviorofthesystemasafunctionofUandVisdespictedin g.4.

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2 12468FIG.4.Schematicevolutionofferromagnetismwiththeinteractions.PM:paramagneticphase,FM↑(FM↓):magneticpolarizationoftheinteractingsystemsmaller(bigger)thanthatofthefreesystem;FM:fullypolarized nalstate.

Pomeranchuckinstabilitiesarefoundsystematicallyundertheappropriateconditionsintheparamagneticzoneofthephasediagram.ByincreasingUandkeepingVconstant,theyenterintothephasedenotedbyFM↓in g.4changingitintoaparamagneticphase.FinallythereisacriticalvalueofUforwhichferromagnetismprevailsandthedeformationdissapears.

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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

Inconclusionwehaveshownthatexchangeinteractionsrenormalizet′tosmallervalues.Aninmediateconsequenceofthisisthat,inoursearchformicroscopicmodelsofthecuprates,oneshouldstartthecomputationswithabiggervalueoft′toaccountforaphenomenologically ttedvalueoft′.Thee ectisdoping–dependentandshouldbestrongerintheunderdopedsituationwherescreeningislesse ective.InthisregimeitwillincreasethenestingoftheFermisurfaceandenhanceantiferromagneticinstabilities.Therenormalizationofthet′parametermayalsoexplaintheabsenceofferromagneticphasesinsomerealsystemsdescribedbythet t′–Hubbardmodel,andrecentmeassurementsofelectron–likeFermisurfacesinsomecuprates.

PomeranchuckinstabilitiesarefoundastheresponseofthesystemtosmallimpuritieswhentheFermisurfaceliesattheVanHove llingandcanberegardedasaninstabilityoftheVanHovelevel.TheycompetewithferromagnetismanddissapearatacriticalvalueU(V).

Althoughtheresultspresentedinthispaperaremean eldresults,webelievethatthemainfeatureswillsurvivethetestwithmoreaccuratemethodsandthatexchangeinteractionsshouldbeincluded–orcheckedtobenegligible–inHubbardrelatedstudies.

Acknowledgements.WeareverygratefultoF.Guineaforvaluablediscussions.FinancialsupportfromMEC(Spain)throughgrantPB96/0875andCAM(Madrid)throughgrant07/0045/98is

acknowledged.