Effect of the additional second neighbor hopping o

arXiv:cond-mat/0203345v1[cond-mat.str-el]17Mar2002Effectoftheadditionalsecondneighborhoppingonthechargedynamicsinthet-JmodelFengYuan1andShipingFeng1,2,31DepartmentofPhysics,BeijingNormalUniversity,Beijing100875,China2TheKeyLaboratoryofBeamTechnologyandMaterialModificationofMinistryofEducation,BeijingNormalUniversity,Beijing100875,China3NationalLaboratoryofSuperconductivity,AcademiaSinica,Beijing100080,ChinaAbstractTheeffectoftheadditionalsecondneighborhoppingt′onthechargedy-namicsofthet-Jmodelintheunderdopedregimeisstudiedwithinthefermion-spintheory.Theconductivityspectrumofthet-t′-Jmodelshowsthelow-energypeakandunusualmidinfraredband,whiletheresistivityexhibitsanearlytemperaturelineardependencewithdeviationatlowtemperatureintheunderdopedregime.Althoughthequalitativefeatureofthechargedynamicsinthet-t′-Jmodelisthesameasinthecaseofthet-Jmodel,theadditionalsecondneighborhoppingt′leadstoaclearshiftofthepositionofthemidinfraredbandtothehigherenergiesintheconductivityspectrum,andsuppresstherangeofthedeviationfromthetemperaturelineardependenceintheresistivity.71.27.+a,74.72.-h,72.10.-dTypesetusingREVTEX1Ithasbecomeclearinthepastseveralyearsthatcopperoxidematerialsshowmanyun-usualnormal-stateproperties[1].Thenormal-statepropertiesexhibitanumberofanoma-louspropertiesinthesensethattheydonotfitintheconventionalFermi-liquidtheory,andsomepropertiesmainlydependontheextentofdopings[1].Amongthestrikingfeaturesoftheanomalousnormal-statepropertiesstandsouttheextraordinarychargedynamics,whichismanifestedbytheopticalconductivityandresistivity[2].Ithasbeenshownfromtheexperiments[1–5]thattheopticalconductivityspectrumofcopperoxidematerialsshowsthenon-Drudebehavioratlowenergiesandexoticmidinfraredbandinthecharge-transfergap,whiletheresistivityexhibitsalinearbehaviorinthetemperatureintheoptimallydopedregimeandanearlytemperaturelineardependencewithdeviationsatlowtempera-turesintheunderdopedregime.Thesinglecommonfeatureofcopperoxidematerialsisthetwo-dimensional(2D)CuO2plane[1,2],anditseemsevidentthattheanomalousbehaviorsaregovernedbythisplane.SincethecopperoxidesuperconductorsaredopedMottinsu-lators,manyauthors[6,7]havesuggestedthattheessentialphysicsofthesematerialscanbeeffectivelydescribedbythe2Dt-Jmodelactingonthespacewithnodoublyoccupiedsites,wheretisthenearestneighborhoppingmatrixelement,andJisthenearestneighbormagneticexchangeinteraction.Thismodelhasbeenusedtostudythechargedynamicsofcopperoxidematerialsintheunderdopedregime,andtheresultsobtained[8–11]fromtheanalyticalmethodsandnumericalsimulationsareinqualitativeagreementwiththeexperiments[1–5].However,therecentangle-resolvedphotoemissionspectroscopymeasurements[12]oncopperoxidematerialsshowthatalthoughthehighestenergyfilledelectronbandiswellde-scribedbythet-Jmodelinthedirectionbetweenthe(0,0)pointandthe(π,π)pointinthemomentumspace,butboththeexperimentaldatanear(π,0)pointandoveralldispersionmaybeproperlyaccountedbygeneralizingthet-Jmodeltoincludethesecond-andthird-nearestneighborshoppingtermst′andt′′.ThesephotoemissionresultsalsoshowthattheelectronbandwidthisreducedfromtheseveraleVexpectedfromthebandtheorytoofor-derJ,whichindicatesthatthecouplingoftheelectrontotheantiferromagneticbackground2playsanimportantroleintheelectronicstructure[12].Ontheotherhand,thechargeresponseisapowerfulprobeforthesystemsofinteractingelectrons,andprovidesveryde-tailedinformationsoftheexcitations,whichinteractwithcarriersinthenormal-state[1–5].Itisbelievedthatbothexperimentsfromtheangle-resolvedphotoemissionspectroscopymeasurementsandchargeresponseproduceinterestingdatathatintroduceimportantcon-straintsonthemicroscopicmodelsandtheories.Inthiscase,anaturalquestioniswhatistheeffectoftheseadditionalhoppingsonthechargedynamicsofthet-Jmodel.Inthispaper,westudythisissuewithint-t′-Jmodel.Ourresultsindicatethattheconductivityspectrumofthet-t′-Jmodelshowsthelow-energypeakandunusualmidinfraredband,whiletheresistivityexhibitsanearlytemperaturelineardependencewithdeviationatlowtemperatureintheunderdopedregime.Althoughthesequalitativefeatureofthechargedy-namicsinthet-t′-Jmodelisthesameasinthecaseofthet-Jmodel[8–11],theadditionalsecondneighborhoppingt′leadstoaclearshiftofthepositionofthemidinfraredbandtothehigherenergiesintheconductivityspectrum,andsuppresstherangeofthedeviationfromthetemperaturelineardependenceintheresistivity.Webeginwiththet-t′-Jmodeldefinedonasquarelattice,H=−tXiˆησC†iσCi+ˆησ+t′XiˆτσC†iσCi+ˆτσ+μXiσC†iσCiσ+JXiˆηSi·Si+ˆη,(1)whereˆη=±ˆx,±ˆy,ˆτ=±ˆx±ˆy,C†iσ(Ciσ)istheelectroncreation(annihilation)operator,Si=C†iσCi/2arespinoperatorswithσ=(σx,σy,σz)asthePaulimatrices,andμisthechemicalpotential.Thestrongelectroncorrelationinthet-Jandt-t′-Jmodelmanifestsitselfbythiselectronsingleoccupancyon-sitelocalconstraint[6,7],andthentheon-sitelocalconstraintshouldbetreatedproperly.Recentlyafermion-spintheorybasedonthecharge-spinseparation[13,14],Ci↑=h†iS−iandCi↓=h†iS+i,hasbeenproposedtoincorpratethison-sitelocalconstraint,wherethespinlessfermionoperatorhidescribesthecharge(holon)degreesoffreedom,whilethepseudospinoperator