Singular or non-Fermi liquids

C.M.Varmaetal./PhysicsReports361(2002)267–417269

1.Introduction

1.1.Aimandscopeofthispaper

Inthelasttwodecadesavarietyofmetalshavebeendiscoveredwhichdisplaythermodynamicandtransportpropertiesatlowtemperatureswhicharefundamentallydi erentfromthoseoftheusualmetallicsystemswhicharewelldescribedbytheLandauFermi-liquidtheory.TheyhaveoftenbeenreferredtoasNon-Fermiliquids.Afundamentalcharacteristicofsuchsystemsisthatthelow-energypropertiesinawiderangeoftheirphasediagramaredominatedbysingularitiesasafunctionofenergyandtemperature.Sincetheseproblemsstillrelatetoaliquidstateoffermionsandsinceitisnotagoodpracticetonamethingsafterwhattheyarenot,weprefertocallthemsingularFermiliquids(SFL).

ThebasicnotionsofFermi-liquidtheoryhaveactuallybeenwithusatanintuitivelevelsincethetimeofSommerfeld:Heshowedthatthelinearlow-temperaturespeciÿcheatbehaviorofmetalsaswellastheirasymptoticlow-temperatureresisitivityandopticalconductivitycouldbeunderstoodbyassumingthattheelectronsinametalcouldbethoughtofasagasofnon-interactingfermions,i.e.,intermsofquantummechanicalparticleswhichdonothaveanydirectinteractionbutwhichdoobeyFermistatistics.Meanwhile,Paulicalculatedthattheparamagneticsusceptibilityofnon-interactingelectronsisindependentoftemperature,alsoinaccordwithexperimentsinmetals.Atthesametimeitwasunderstood,atleastsincetheworkofBlochandWigner,thattheinteractionenergiesoftheelectronsinthemetallicrangeofdensitiesarenotsmallcomparedtothekineticenergy.Therationalizationforthequalitativesuccessofthenon-interactingmodelwasprovidedinamasterlypairofpapersbyLandau[152,153]whoinitiallywasconcernedwiththepropertiesofliquid3He.Thisworkepitomizedanewwayofthinkingaboutthepropertiesofinteractingsystemswhichisacornerstoneofourunderstandingofcondensedmatterphysics.Thenotionofquasiparticlesandelementaryexcitationsandthemethodologyofaskingusefulquestionsaboutthelow-energyexcitationsofthesystembasedonconceptsofsymmetry,withoutworryingaboutthemyriadunnecessarydetails,isepitomizedinLandau’sphenomenologicaltheoryofFermiliquids.Themicroscopicderivationofthetheorywasalsosoondeveloped.

OurperspectiveonFermiliquidshaschangedsigniÿcantlyinthelasttwodecadesorso.Thisisduebothtochangesinourtheoreticalperspective,andduetotheexperimentaldevel-opments:ontheexperimentalside,newmaterialshavebeenfoundwhichexhibitFermi-liquidbehaviorinthetemperaturedependenceoftheirlow-temperaturepropertieswiththecoe cientsoftenafactoroforder103di erentfromthenon-interactingelectronvalues.Theseobser-vationsdramaticallyillustratethepowerandrangeofvalidityoftheFermi-liquidideas.Ontheotherhand,newmaterialshavebeendiscoveredwhosepropertiesarequalitativelydif-ferentfromthepredictionsofFermi-liquidtheory(FLT).Themostprominentlydiscussedofthesematerialsarethenormalphaseofhigh-temperaturesuperconductingmaterialsforarangeofcompositionsneartheirhighestTc.Almosteveryideadiscussedinthisreviewhasbeenusedtounderstandthehigh-Tcproblem,butthereisnoconsensusyetonthesolution.

IthasofcoursebeenknownforalongtimethatFLTbreaksdowninthe uctuationregimeofclassicalphasetransitions.Thisbreakdownoccursinamoresubstantialregionofthephase