General Relativity and the Cuprates

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1、GeneralRelativityandtheCupratesGaryT.HorowitzandJorgeE.SantosDepartmentofPhysics,UCSB,SantaBarbara,CA93106,USAgary@physics.ucsb.edu,jss55@physics.ucsb.eduAbstractWeaddaperiodicpotentialtothesimplestgravitationalmodelofasuperconductorandcomputetheopticalconductivity.Inadditiontoasuper uidcomponen

2、t,wendanormalcomponentthathasDrudebehavioratlowfrequencyfollowedbyapowerlawfall-o.BoththeexponentandcoecientofthepowerlawaretemperatureindependentandagreewithearlierresultscomputedaboveTc.Theseresultsareinstrikingagreementwithmeasurementsonsomecuprates.Wealsondagap
=4:0Tc,arapidlydecreasings

3、catteringrate,andmissingspectralweight"atlowfrequency,allofwhichalsoagreewithexperiments.arXiv:1302.6586v1[hep-th]26Feb20131Contents1Introduction22Gravitationalmodel33Backgrounds54Conductivity94.1Lowfrequencyregion...................................104.2Powerlaw.................................

4、........134.3Sumrule..........................................144.4Resonance.........................................165Discussion17ATherstlawforblackholeswithvaryingchemicalpotential181IntroductionGauge/gravitydualityhasprovidedapowerfulnewtooltoanalyzecertaincondensedmattersys-tems.Inparticul

5、ar,itcanbeusedtocalculatetransportpropertiesofstronglycorrelatedsystemsatnitetemperature.Remarkably,thisisachievedbymappingtheproblemtoagravitationalprobleminonehigherdimension.Sincethesystemofinterestlivesinonedimensionlessthanthegravitationalproblembeingsolved,thisapproachisoftencalledhologra

6、phic.Theopticalconductivityinasimpleholographicmodelofa2+1dimensionalconductorwasrecentlystudiedincludingtheeectsofalattice[1].Earlierstudiesassumedtranslationinvariancewhichimpliedmomentumconservation.Inthatcase,thechargedparticlescannotdissipatetheirmomentumsotherealpartoftheopticalconductivi

7、tyalwayscontainsadeltafunctionatzerofrequencyre ectinginniteDCconductivity.Withthelatticeincluded,thedeltafunctionisresolved.ItwasfoundthatatlowfrequencytheconductivityfollowsthesimpleDrudeform,butatintermediatefrequency,it