Ladders Reveal a Complex Interplay between a Spin-

arXiv:cond-mat/9908250v1[cond-mat.str-el]17Aug1999EXPERIMENTSONLADDERSREVEALACOMPLEXINTERPLAYBETWEENASPIN-GAPPEDNORMALSTATEANDSUPERCONDUCTIVITYElbioDAGOTTONationalHighMagneticFieldLabandDepartmentofPhysics,FloridaStateUniversity,Tallahassee,FL32306,USAByinvitationforReportsofProgressinPhysicsInrecentyears,thestudyofladdermaterialshasdevelopedintoawell-establishedareaofresearchwithinthegeneralcontextofStronglyCorrelatedElectrons.Thisefforthasbeentriggeredbyanunusualcross-fertilizationbetweentheoryandexperiments.Inthispaper,themainexperimentalresultsobtainedinthecontextofladdersarereviewedfromtheperspectiveofatheorist.Emphasisisgiventothemanysimilaritiesbetweenthetwo-dimensionalhigh-Tccupratesandthetwo-legladdercompounds,includingSr14−xCaxCu24O41(14-24-41)whichhasasuperconductingphaseathighpressureandasmallholedensity.Examplesofthesesimilaritiesincluderegimesoflinearresistivityvstemperatureinmetallicladdersandanormalstatewithspin-gaporpseudogapcharacteristics.Somecontroversialresultsinthiscontextarealsodiscussed.Itisremarkedthattheladder14-24-41isthefirstsuperconductingcopper-oxidematerialwithanon-square-latticelayeredarrangement,andcertainlymuchcanbelearnedfromacarefulanalysisofthiscompound.Ashortsummaryofthemaintheoreticaldevelopmentsinthisfieldisalsoincluded,aswellasabriefdescriptionofthepropertiesofnon-copper-oxideladders.Suggestionsbytheauthoronpossibleexperimentsaredescribedinthetext.Overall,itisconcludedthattheenormousexperimentaleffortcarriedoutonladdershasalreadyunveiledquitechallengingandinterestingphysicsthataddstotherichbehaviorofelectronsintransition-metal-oxides,andinadditioncontributestotheunderstandingofthetwo-dimensionalcuprates.However,stillconsiderableworkneedstobecarriedouttofullyunderstandtheinterplaybetweenchargeandspindegreesoffreedominthesematerials.CONTENTS1.Introduction............................................................................................................................................12.TheoreticalAspects:aBriefSummary.............................................................................................32.1UndopedSpinLadderModels............................................................................................................32.2Hole-dopedSpinLadderModels........................................................................................................43.ExperimentalResults............................................................................................................................53.1TheCu-oxideLadderCompoundSrCu2O3.......................................................................................53.1.1DopingofSrCu2O3withZinc...................................................................................................63.2ThemetallicladdercompoundLa1−xSrxCuO2.5...............................................................................73.3TheSuperconductingLadderCompoundSr14−xCaxCu24O41...........................................................83.3.1SuperconductivityinDoped14-24-41withx=13.6..................................................................83.3.2SuperconductivityinDoped14-24-41withx=11.5..................................................................93.3.3OpticalConductivityσ(ω)........................................................................................................113.3.4NuclearMagneticResonance....................................................................................................123.3.5InelasticNeutronScattering.....................................................................................................133.3.6PhotoemissionandAngle-ResolvedPhotoemissionA(p,ω).....................................................133.4TheStrong-CouplingLadderCompoundCu2(C5H12N2)2Cl4...........................................................143.5Vanadium-basedLadderCompoundCaV2O5...................................................................................143.6TheLadderCompoundKCuCl3.......................................................................................................154.Conclusions............................................................................................................................................155.Acknowledgements...............................................................................................................................16I.INTRODUCTIONThetheoreticalandexperimentalstudyofmaterialswithanionicstructurecontainingdominantpatternsintheshapeof“ladders”hasrecentlyattractedaconsid-erableattentioninthecontextofStronglyCorrelatedElectronsandCondensedMatterphysics.Then-leglad-dersaredefinedasnparallelchainsofions,withbondsamongthemsuchthattheinterchaincouplingiscompa-rableinstrengthtothecouplingsalongthechains.Theparticularcaseofn=2motivatestheuseofthename“ladder”forthisgeometry.Thecouplingbetweenthe1twochainsthatparticipateinthisstructureisthrough“rungs”,languagealsoextendedtothen-legsystems.Avastliteratureonthissubjecthasalreadya