Charge dynamics of Ca_{2-x}Na_{x}CuO_{2}Cl_{2} as a correlated electron system with the ide

We report the reflectivity and the resistivity measurement of Ca_{2-x}Na_{x}CuO_{2}Cl_{2} (CNCOC), which has a single-CuO2-plane lattice with no orthorhombic distortion. The doping dependence of the in-plane optical conductivity spectra for CNCOC is qualit

ChargedynamicsofCa2 xNaxCuO2Cl2asacorrelatedelectronsystemwiththeideal

tetragonallattice

K.Waku,1, T.Katsufuji,2,3Y.Kohsaka,1T.Sasagawa,1H.Takagi,1,4

H.Kishida,1,3H.Okamoto,1M.Azuma,5,3andM.Takano5,4

1

arXiv:cond-mat/0408423v1 [cond-mat.supr-con] 19 Aug 2004

DepartmentofAdvancedMaterialsScience,UniversityofTokyo,Chiba277-8562,Japan

2

DepartmentofPhysics,WasedaUniversity,Tokyo169-8555,Japan

3

PRESTO,JapanScienceandTechnologyCorporation,Saitama332-0012,Japan4

CREST,JapanScienceandTechnologyCorporation,Saitama332-0012,Japan5

InstituteofChemicalResearch,KyotoUniversity,Kyoto611-0011,Japan

(Dated:February2,2008)

Wereportthere ectivityandtheresistivitymeasurementofCa2 xNaxCuO2Cl2(CNCOC),whichhasasingle-CuO2-planelatticewithnoorthorhombicdistortion.Thedopingdependenceofthein-planeopticalconductivityspectraforCNCOCisqualitativelythesametothoseofothercuprates,butaslightdi erencebetweenCNCOCandLSCO,i.e.,theabsenceofthe1.5eVpeakinCNCOC,canbeattributedtothesmallercharge-stripeinstabilityinCNCOC.ThetemperaturedependenceoftheopticalconductivityspectraofCNCOChasbeenanalyzedbothbythetwo-componentmodel(Drude+Lorentzian)andbytheone-componentmodel(extended-Drudeanalysis).Thelatteranaly-sisgivesauniversaltrendofthescatteringrateΓ(ω)withdoping.ItwasalsofoundthatΓ(ω)showsasaturationbehaviorathighfrequencies,whoseoriginisthesameasthatofresistivitysaturationathightemperatures.

I.

INTRODUCTION

Therehasbeenalonghistoryofdiscussionsaboutthein-planechargedynamicsofcupratesuperconduc-tors.Itisbelievedthatthein-planechargedynamicsofcupratesuperconductorsisdominatedbyasmallamountofholesintroducedintoaCuO2plane,whichistheoret-icallyrepresentedbyatetragonallatticeofCu2+ions(3d9)withstrongon-sitecoulombrepulsion.However,mostofthecupratesuperconductorshaveothercharac-teristicsthatmakethesystemawayfromsuchasimpletwodimensionaltetragonallattice.First,thereisoftenadi erenttypeoforthorhombicdistortionineachsys-tem:La2 xSrxCuO4(LSCO)hasabucklingofCuO6octahedra,1YBa2Cu3O7(YBCO)hasCuOchainsbe-tweenCuO2planes,andBi2Sr2CaCu2O8(BSCCO)hastheanisotropicmodulationofBiOlayers,2allofwhichintroducesorthorhombicityintothesystems.Second,thereisaninstabilityofthestripeformationintheCuO2plane,whichisparticularlystrongin3Althoughitisnotestablishedwhethersuchastripeinstabilityisanintrinsicnatureofthetetragonallattice,itisexperimen-tallyshownthattheorthorhombicdistortionlargelyaf-fectsthestripeformationinLSCO.4Thisinstabilityalsocomplicatesthesystemanditsphysics.Finally,YBCOandBSCCOhasabilayerstructureofCuO2planes,anditisknownthattheinter-bilayercouplingcannotbeig-noredinsuchsystems.5Thisdi erencebetweensingle-layerLSCOandbilayerYBCOorBSCCOmakesitdi -culttocomparetheirchargedynamicsinaquantitativeway.

Re ectivitymeasurementisapowerfultechniquetoinvestigatethechargedynamicsofmetalsandhasbeenusedforthestudyofboththein-planeandtheout-of-planechargedynamicsincupratesuperconductors.As

anoverallfeature,thedopingdependenceandthetem-peraturedependenceofthein-planeopticalspectraaresimilarinallsystems,6BSCCO,7and8Namely,upondoping,thepeakaround2eVintheopticalconductivityspectrum,whichcorrespondstothecharge-transfer(CT)excitationbetweentheCu3dandtheoxy-gen2plevels,decreasesinitsintensitywhereasaquasi-Drudepeak,whicharisesfromtheitinerantmotionofthecarriers,evolvesbelow1.0eV.However,severaldetailsaredi erentbetweenthespectraofthesesystems.Itwaspointedoutthattheshapeofthequasi-Drudepeakbelow1.0eVisslightlydi erentbetweenthesethreesystems:Thequasi-DrudespectrumofLSCOhasadiparound0.1eVandcanbeseparatedintoasharpDrudecomponentbelow0.1eVandaLorentzianaboveit,whereasthatofBSCCOandYBCOismoresmoothanddoesnotlooklikethesumoftwocomponents.9ItwasalsopointedoutthatthereisapeakexistingbetweentheCTexcitationandthequasi-DrudepeakintheLSCOspectraaround1.58whichisabsentinothertwosystems.Thesedi erencesshouldcomefromthedi erenceinthecrystalstructureasdescribedabove,butithasyettobeunder-stoodhowthedeviationfromatetragonallatticea ectsthein-planechargedynamics.

Ca2 xNaxCuO2Cl2(CNCOC)isoneofthebestsys-temsinthatsensetoinvestigatethechargedynamicsofthecorrelatedelectronsystemwithapurelytetragonallattice.Thiscompoundhasasingle-CuO2-planestruc-turewithapicalchlorine10insteadofapicaloxy-genionsinLSCO.Sincethe(Ca,Na)ClplaneseparatingtwoCuO2planeshasamoreioniccharacterthanthe(La,Sr)OplaneinLSCO,itisexpectedthatthecouplingbetweentwoadjacentCuO2planesismuchsmallerinCNCOCthaninLSCO.Inaddition,unlikeLSCO,thereisnobucklingdistortionoftheoctahedralnetworkinCN-COC,thusbeingasimpletetragonalstructure.10These

We report the reflectivity and the resistivity measurement of Ca_{2-x}Na_{x}CuO_{2}Cl_{2} (CNCOC), which has a single-CuO2-plane lattice with no orthorhombic distortion. The doping dependence of the in-plane optical conductivity spectra for CNCOC is qualit

twocharacteristicsmakeCNCOCthebestsystemrepre-sentingtheelectroncorrelationinthepurelytetragonallattice.Previously,itwasdi culttomakesinglecrys-talsofCNCOCbecauseofthenecessityofusinghighpressureevenformakingpolycrystallinesamples.How-ever,recentprogressinmakingsinglecrystalsunderhighpressurehasovercomethisobstacle,11andnowaseriesofsinglecrystalswithvariousdopinglevelinCNCOCcanbegrown,whichislargeenoughinsizeforresistivityandre ectivitymeasurement.Inthispaper,wereporttheresistivityandre ectivitymeasurementofCNCOC.Inparticular,wefocusonthedopingandtemperaturedependenceofthein-planechargedynamicsinthenor-malphasestudiedbyopticalmeasurement.

II.EXPERIMENTAL

SinglecrystalsofCNCOCweregrownbya uxmethodunderhighpressures.ThedetailsofcrystalgrowthhavealreadybeenpublishedinRef.11.SincetheNadopedsamples(x>0)arehighlyhygroscopic,aspecialat-tentionwaspaidnottoexposethesampletotheairinthepreparationandmeasurement.Thein-planere-sistivitywasmeasuredbyastandardfour-probetech-nique,whiletheout-of-planeresistivitywasmeasuredbyaquasi-Montgomerytechnique.Inbothcases,evapo-ratedgoldwasusedastheelectrodes.Themeasure-mentswereperformedinthevacuumconditionwithasampleholderthatwasspeciallydesignednottoexposethesampletotheairduringthepreparationandmea-surement.There ectivityspectraweremeasuredonthecleavedsurface,whichwaspreparedintheargon- lledglovebox.WeusedaFourier-typeinterferometerbe-tween70meVand1.2eVandagratingtypespectrome-terbetween0.75eVand5eV.Thesizeofthesamplewemeasuredwas1mm×1mmatbest,andtheoptically atareaismuchsmallerthanthat.Thus,allthemeasure-mentsweredoneunderthemicroscopeattachedtothespectrometer,withatypicalspotsizeof80µm×80µm.Becauseofthissizelimitation,themeasurementinthefar-infraredregion(below70meV)cannotbemadewithourmeasurementsystem.Forthemeasurementatroomtemperature,thesamplewasplacedinasealedsmallbox lledwithargongasequippedwithanopticalwindow.Almirrorwasalsoplacedadjacenttothesampleasaref-erence.Wemeasuredthere ectivityatlowtemperaturesbetween70meVand1.2eVwithaconduction-typecryo-statinavacuumcondition.Toobtaintheabsolutevalueofthere ectivity,weusedthespectrumatroomtem-perature,whichwasseparatelymeasuredasdescribedabove,asareference.Wealsomeasuredthere ectivityoftheundopedsampleintheenergyrange5-34eVusingthesynchrotronsourceattheInstituteforMolec-ularScience(UV-SOR).Opticalconductivityspectrumwascalculatedfromthemeasuredre ectivityspectrumusingKramers-Kronigrelation.WeusedHagen-Rubensextrapolationforh¯ω<0.1eVandtheω 4extrapolation

2

above34eV.Wealsomadeothertypesofextrapolationforh¯ω<0.1eVandcheckthedi erenceofopticalcon-ductivityspectra,whichwillbediscussedinthefollowingsections.

III.RESISTIVITYMEASUREMENTS

Figure1showsthetemperaturedependenceofthein-planeresistivity(ρab)forCNCOC(x≥0.06).Theab-solutevalueandthetemperaturedependenceofρabfor

CNCOCissimilartothatofLSCOatthesamedop-inglevelforx=0.08andx=0.10.12Forx=0.06,however,theabsolutevalueofρabismuchlargerthanthatoftheLSCOcounterpart.Wespeculatethatthelargevalueofρabforx=0.06iscausedbythemixingoftheout-of-planecomponent,whichoftenhappensintheresistivitymeasurementofthinsampleswithlargeanisotropy.Itshouldbenotedthatsuchamixingbarelya ectstheresultoftheout-of-planeresistivity.Fig-ure2showsthetemperaturedependenceoftheout-of-planeresistivity(ρc)forCNCOC.Themagnitudeofρcatroomtemperature12isabout50timeslargerthanthatofLSCOatthesamedopinglevel.Asaresult,theratioof4anisotropyintheresistivity(ρc/ρab)amountsto～10inCNCOC.Thislargerabsolutevalueofρccanbeattributedtothesmallercouplingoftwoadja-centCuO2planesinCNCOC,whichareseparatedbytheCa(Na)Clplanewithahighlyioniccharacter.Bycontrast,thetemperaturedependenceofρcinCNCOCissmallerthanthatinLSCO.Forexample,atx=0.10,theresistivityratioρc(50K)/ρc12(290K)isabout1.8forCN-COCwhereas2.0forLSCO.Thisdiscrepancybetweentheabsolutevalueandthetemperaturedependenceofρccanhardlybeexplainedbyaconventionalsemiconductormodel.Onepossibleexplanationisthatthetemperaturedependenceofρcisdominatedbythesizeoftheso-calledpseudogapasproposedpreviously.13,14Thepseudogaphasbeenobservedinvariousexperiments,forexample,NMR,15photoemissionspectroscopy,16andevenopticalmeasurement.17,18ThesizeofthepseudogapshouldscalewiththemaximumTcofeachsystem,whichis28KforCNCOCand38KforLSCOinthepresentcase.There-fore,itisexpectedthatthesizeofthepseudogapinLSCOislargerthanthatinCNCOC,consistentwiththetemperaturedependenceofρc.Asamorequanti-tativeanalysis,weestimatedthesizeofthepseudogapfromArreniusplotofρc(T).AsshowninFig.2,theactivationenergyofρc(T),whichscaleswiththesizeofthepseudogap,isabout4.5KinCNCOC.ForBSSCO,theactivationenergyofρc(T)isabout200K.19Suchahugedi erenceofthesizeofthepseudogapestimatedfromρc(T)mayexplainwhyTcofCNCOCissolowcomparedwithBSSCO.

We report the reflectivity and the resistivity measurement of Ca_{2-x}Na_{x}CuO_{2}Cl_{2} (CNCOC), which has a single-CuO2-plane lattice with no orthorhombic distortion. The doping dependence of the in-plane optical conductivity spectra for CNCOC is qualit

FIG.1:Thetemperaturedependenceofthein-planeresistiv-ityρabforCNCOCwithx=0.08and0.10.Theinsetshows

ρabofx=0.06,togetherwiththoseofx=0.08and0.10.

FIG.2:Thetemperaturedependenceoftheout-of-planeresistivityρcforCNCOC.TheinsetistheArreniusplotofρcforx=0.06.

IV.

THEDOPINGDEPENDENCEOFTHE

OPTICALSPECTRA

Thedopingdependenceofthere ectivityofCNCOCisshowninFig.3.Theopticalconductivityspectraderivedfromthesere ectivitydataareshowninFig.4.Theoverallfeaturesofthespectrumanditsdopingdependencearethesameasthoseofothercuprates:asharppeakat2.1eVissuppressedandthequasi-Drudespectrumbelow1.0eVevolveswithincreasingx.How-

3

FIG.3:(Coloronline)Thedopingdependenceofre ectivityatroomtemperature.

ever,thereareseveraldi erencesbetweenCNCOCand

LSCO.Figure5compares20theopticalconductivityspec-traofCNCOCandLSCOwiththesamedopinglevel.Ascanbeseen,CNCOCalwayssurpassesLSCOinthespectralweightoftheDrudespectrumbelow1.5eV.An-otherdi erenceisthatthereisasmallpeakat1.5eV(shownbyatriangle)intheLSCOspectra,butsuchapeakishardlyseenintheCNCOCspectra.

InFig.5,theopticalconductivityspectrumderivedfromthere ectivityspectrumwithalinearextrapolationbelow0.1eVisalsoplottedforx=0.08(thesolidline).Ascanbeseen,thereisasmalldi erencebetweenthosewithaHagen-Rubensandalinearextrapolationsbelow0.2eV.However,thisdi erenceisnotlargeenoughtoqualitativelya ectthefollowingdiscussions.

Tomakemorequantitativediscussionsaboutthedif-ferenceandthesimilarityofthespectrabetweenCNCOCandLSCO,thee ectivenumberofelectrons,Ne wases-timatedinthefollowingway,

N2mV

e =

We report the reflectivity and the resistivity measurement of Ca_{2-x}Na_{x}CuO_{2}Cl_{2} (CNCOC), which has a single-CuO2-plane lattice with no orthorhombic distortion. The doping dependence of the in-plane optical conductivity spectra for CNCOC is qualit

FIG.4:(Coloronline)Thedopingdependenceofopticalconductivityatroomtemperature.

CuO2planebetweenthesetwosystemsisthebucklingoftheCuO6octahedraandastripeinstability,bothofwhichexistonlyinLSCO.ItshouldbenotedherethatthebucklingoftheCuO6octahedradisappearsforx>0.20inLSCO,1wherethe1.5eVpeakstillsurvives.8Therefore,itisplausibletoassignthe1.5eVpeakintheopticalconductivityofLSCOastheexcitationassociatedwiththechargestripe.Thisassignmentcanalsoexplainwhythe1.5eVpeakdoesnotexistineitherYBCO6orBSCCO.7

InFig.

6,itisalsofoundthatNe withh¯ωc=1eV,whichcorrespondstotheDrudeweightofthesystems,ofCNCOCislargerthanthatofLSCO.Thisresultiscoun-terintuitive,ifonerecallsthephasediagramofthesetwosystems;LSCObecomessuperconductingforthesmallervalueofx(≥0.06)thanCNCOC(≥0.09).10ThisismoreclearlyseeninFig.7,whereNe andthesuperconduct-ingtransitiontemperatureTcofeachsampleareplotted.Ascanbeseen,CNCOCandLSCOfollowthedi erenttrend,indicatingthatNe isbynomeansthedominantparameterofTc.

Sincethesetwosystems,CNCOCandLSCO,haveasimilarcrystalstructure(thesingleCuO2plane),there-sultisrathersurprising.OnepossibleexplanationisthatnotalloftheDrudespectrumbelow1.0eVcontributestothesuperconductivity.Inotherwords,thespectralweightthatcondensatestothesuper uid,whichdomi-natesthetransitiontemperature,isonlyafractionofthespectralweightbelow1.0eV.Thisinterpretationsug-geststhetwo- uidnatureofthequasi-Drudespectrumbelow1.0eV,buthowthespectrumisdividedintotwocomponentsremainsunclear.

FIG.5:(Coloronline)Comparisonoftheopticalconductiv-itybetweenLSCOandCNCOC.ThedataofLSCOisfromRef.20.ThedataofCNCOC(thedottedline),whichisderivedfromthere ectivityspectrumwithaHagen-Rubensextrapolation,ispreviouslyshowninFig.4.Theopticalconductivityspectrumderivedfromthere ectivityspectrumwithalinearextrapolationbelow0.1eVisalsoplottedforx=0.08(thesolidline).V.

THETEMPERATUREDEPENDENCEOF

THEOPTICALSPECTRA

Figure8showsthetemperaturedependenceoftheop-ticalconductivityspectraforCNCOCwithx=0.06,0.08,and0.10(solidsymbols).ItiswellknownthattheDrude-likespectrumbelow1eVinthecupratesu-perconductorscannotbe ttedbyasingleDrudeform,andtherehavebeenalotofargumentsaboutwhethertheone-componentmodel(theso-calledextendedDrudemodel)orthetwo-componentmodel(theDrudeandLorentzianmodel)isappropriatetoexplainsuchaspec-trum.Here,weanalyzetheexperimentaldataofCN-COCinbothways.

First,21thespectrawereanalyzedbythetwo-componentmodel,i.e.,thesumofaDrudecomponentandaLorentzianinthefollowingway;

σ(ω)=σD(ω)+σL(ω)

(2)

σω2D(ω)=

D

ω2+Γ2(3)

D

σ(ω)=

SLLω2L

(ω2 ω2)2+ω2Γ2(4)

LL

We report the reflectivity and the resistivity measurement of Ca_{2-x}Na_{x}CuO_{2}Cl_{2} (CNCOC), which has a single-CuO2-plane lattice with no orthorhombic distortion. The doping dependence of the in-plane optical conductivity spectra for CNCOC is qualit

FIG.6:Ne ofCNCOCandLSCOwiththe

cut-o energyh¯

ωc=1eVand3.5eV.FIG.7:TherelationbetweenNe at1eVandthesuper-conductingtransitiontemperatureTcofLSCOandCNCOC.Dottedlinesareguidetoeyes.

Here,thereare ve ttingparameters(twofortheDrudeandthreefortheLorentzian),theplasmafre-quencyoftheDrudecomponentωD,thescatteringrateoftheDrudecomponentΓD,theoscillatorstrengthoftheLorentzianSL,thepeakpositionoftheLorentzianωL,andthescatteringrateoftheLorentzianΓL.Theresultofthe ttingtoeachspectrum

isquitesatisfac-tory,asshownbythesolidlinesinFig.8.Thedoping-andthetemperature-dependenceofthe veparametersaresummarizedinFig.9.Ascanbeseen(1)ωDbarelychangeswithdoping,butdecreaseswithdecreasingtem-

FIG.8:(Coloronline)Theclosedsymbolsaretheoptical

conductivityobtainedfromthere ectivityspectra.Thesolidlinesaretheresultofthe ttingbythesumofaDrudeandaLorentziancomponents.ThedottedlinesaretheDrudecom-ponents,andthedot-dashedlinesaretheLorentziancompo-nents.

)Ve(DDωTemperature(K)

Temperature(K)

Temperature(K)

Temerature(K)

Temperature(K)

FIG.9:(Coloronline)Thedoping-andthetemperature-dependenceofthe veparameters,ωD,ΓD,SL,ωL,andΓLderivedfromthe ttingoftheopticalconductivityspectrum.The ttingfunctionisshowninthetext[Eq.(2),(3),(4)].

perature(2)ΓDdecreaseswithincreasingdopingandwithdecreasingtemperature(3)SLincreaseswithin-creasingdopingbutdoesnotchangewithtemperature(4)ωLdecreaseswithincreasingdopingandwithdecreas-ingtemperature(5)ΓLbarelychangeswithdopingandtemperature.

Therearevarioustheoreticalstudiesonthestronglycorrelatedsystemswithdoping.22,23,24However,thepresentexperimentalresultshaveseveralsigni cantdis-crepancieswiththosetheoreticalstudies.First,mostofthetheoriespredicttheincreaseoftheDrudefre-quencyωD(orDrudeweight)withincreasingdopinganddecreasingtemperature,bothofwhichareinconsistent

We report the reflectivity and the resistivity measurement of Ca_{2-x}Na_{x}CuO_{2}Cl_{2} (CNCOC), which has a single-CuO2-plane lattice with no orthorhombic distortion. The doping dependence of the in-plane optical conductivity spectra for CNCOC is qualit

withthepresentexperimentalresult[Fig.

9(a)].Second,thelocalizedstate,whichisrepresentedbyaLorentzianform,usuallyshiftstoahigherenergywithdecreasingtemperature.Thisbehaviorisalsotrueforthetheoreti-calstudiesofthestronglycorrelatedsystemwithin nitedimensions.23However,thepresentexperimentalresultindicatesthatωLratherdecreaseswithdecreasingtem-perature[Fig.9(d)],hardtoreconcilewiththetheories.Thesimilaritybetweenthedoping-andthetemperature-dependenceofΓD[Fig.9(b)]andωL[Fig.9(d)]suggeststhatthespectrumassignedtoaLorenztiancomponent(alocalizedstate)inthis ttingisnotreallyalocalizedstate,butapartofaDrudecomponent(anitinerantstate).Inotherwords,thepresentanalysissuggeststhattheone-componentmodelismoreplausibleto tthedataofCNCOCthanthetwo-componentmodel.

Wealsoanalyzethedatabytheone-componentmodel,i.e.,theextendedDrudemodel.25Inthismodel,allofthespectrumbelow1.0eVisassignedtoanitinerantstate,butthee ectivemassandthescatteringratearebothω-dependentandarederivedbythefollowingexpression,

σ (ω)=

4πne2

ω+iΓ(ω)

,(5)

hereσ (ω)isthecomplexopticalconductivity.Theresult

oftheΓ(ω)atvarioustemperaturesateachxisshowninFig.10.ThereisastrongωdependenceofΓ(ω)ineachxandtemperature.Particularlyatlowfrequency,thescatteringratehasatermalmostproportionaltoω,insuchawaythatΓ(ω)=Γ0+Cω,whichisacommonbehaviorofcupratesuperconductors.25AscanbeseeninFig.10,theω-coe cientinΓ(ω)atlowfrequency,C,isalmosttemperatureindependent,butonlythecon-stanttermΓ0decreaseswithdecreasingtemperature.ItcanalsobeseeninFig.10thatΓ(ω)issaturatedforh¯ω>～0.4eV.Wespeculatethatthisbehaviorissimi-lartothebehaviorofresistivitysaturationobservedinthedcresistivityathightemperatures.26Thisissueisdiscussedinthenextsection.

Figure11comparestheωdependenceofthescatteringrate,Γ(ω),ofCNCOCandYBCO.25Ascanbeseen,Γ(ω)ofCNCOCwithx=0.10andYBCOwithTc=56Kisalmostthesame.ItshouldbenotedthattheratioofTcforCNCOCwithx=0.10(18K)tothemaximumTcofthesameseries(28Kforx=0.15),whichisagoodmeasureoftheholeconcentration,is～0.6,andthisvalueisalmostthesameasthatofYBCOwithTc=56K.ThisindicatesthatΓ(ω)isthesameforthesampleswiththesameholeconcentration,eventhoughthesystemsaredi erent.SuchauniversalityofΓ(ω)withthechangeoftheholeconcentrationshouldbeanintrinsicnatureofaCuO2planewithatetragonallattice.

6

FIG.10:(Coloronline)Theω-dependenceofthescatteringrateΓderivedfromtheextendedDrudeanalysis.

FIG.11:(Coloronline)ComparisonofΓ(ω)betweenCN-COCandYBCO.ThedataofCNCOCisderivedfromtheopticalconductivitiesat200K.ThedataofYBCOisfromRef.25.

VI.DISCUSSION

AsshowninFig.4,therearedistincttwopeaks(AandB)intheopticalconductivityspectrumoftheparentcompoundbetween2and3eV,bothofwhichcanbeas-signedtotheCTexcitation.Withholedoping,however,onlytheApeakdisappearsbuttheBpeaksurvives.Such

We report the reflectivity and the resistivity measurement of Ca_{2-x}Na_{x}CuO_{2}Cl_{2} (CNCOC), which has a single-CuO2-plane lattice with no orthorhombic distortion. The doping dependence of the in-plane optical conductivity spectra for CNCOC is qualit

adopingdependenceofthedouble-peakstructureoftheCTexcitationhasnotbeendiscussedsofar,mainlybe-causethedouble-peakstructureintheparentcompounditselfisnotsoclearinothercupratesuperconductors.ThereareseveralexplanationsforthedoublepeaksoftheCTexcitation.Oneexplanationistoascribethemtothetwokindsofholes,thoseintheZhang-Ricesin-gletband(ZRB)andinthenon-bondingoxygen2pband(NBB).27Here,itshouldbeemphasizedthatbothtwoholebandscanbeobservedintheARPESspectrumoftheparentcompound,andthatbothbandssurviveeveninthehole-dopedsamples.28Therefore,onlythesplit-tingofZRBandNBBcannotexplainthefactthattheApeakdisappearswithholedopingintheopticalspectrum.Wespeculatethattheexcitonice ectbetweenoxygen2pholesandCu3delectronsisessentialtothedopingde-pendenceoftheopticalspectrum,whichinherentlydoesnotexistinthephotoemissionprocess.

Next,theω-dependenceofthescatteringrate,Γ(ω),issaturatedatlargeωasshowninFig.10.ItisnoticeablethatthesaturationvalueofΓisalmostthesameforanytemperatureandx,i.e.,Γ～0.8eV.Thisbehaviorissim-ilarwiththeso-calledresistivitysaturation,whichoccursinthedcresistivityathightemperaturesunderthecon-ditionkF 1,wherekFistheFermiwavenumberand isthemeanfreepathofthecarrier.ConsideringthefactthatthescatteringrateΓhasboththetemperaturedependenceandtheωdependence,Γ(ω)shouldshowasaturationbehaviorjustasΓ(T)doesinthedcresistiv-ity.HereweestimatethesaturationvalueofΓ(ω)ingtherelations =vFτwherevFisFermivelocityandτistherelaxationtimeandvF=h¯kF/m ,wecanrewritetherelationkF =1asΓ=¯h2kF/m .Inthetwo-dimensionalsystem,kFisgivenby(2πnd)1/2(distheinter-planedistanceandnisthecarrierdensity),andthusΓ=n/m ×2π¯h2d.Theunknownparameter,n/m ,wasestimatedfromtheexperimentallyobtainede ectivenumberofelectronsat1eV.TheΓvaluethusde-rivedbecomes0.56eV,0.66eVand0.80eVforx=0.06,0.08and0.10,respectively.TheseareingoodagreementwiththeexperimentallyestimatedvaluesofΓatthesat-urationpoint,indicatingthatthesaturationoftheΓ(ω)hasthesameoriginasthatofΓ(T).

WealsodiscussanotherpossibleinterpretationofthestructureinΓ(ω):IntheARPESdataofthesamecom-pounds,thespectralweightbelow0.4eVisheavilysup-pressed,particularlyaround(π,0)pointinthekspace.Thisbehaviorsuggestseither(a)apseudogap( =0.4eV)opensonthelargeFermisurfacearound(π,0)point,or(b)onlysmallholepocketsexistaround(π/2,π/2)point.If(a)thepseudogappictureiscorrect,thereshouldbeanexcitationbetweenthepseudogapintheop-ticalspectrum,whichcouldappeararound 2 ,andthe“shoulder”around0.4eVinΓ(ω)canbeattributedtotheexcitation.However,thisscenarioisratherun-likely,because(1)asshowninFig.11,theΓ(ω)below0.4eVforx=0.10coincideswiththatofYBCOwithTc=56K,whichdoesnothavesuchalargepseudo-7

gap,and(2)theenergyscaleofthestructureinΓ(ω)barelychanges,orratherincreases,withincreasingholeconcentration,inconsistentwiththebehaviorofthecon-ventionalpseudogapwhoseenergydecreaseswithholedoping.Ontheotherhand,onthebasisof(b)thehole-pocketpicture,thepossible nalstateoftheopticalspec-trumistheupperHubbardband,whichis～2eVabovetheholeband,andthus,therewouldbenoexcitationbe-low1eVexceptforaDruderesponseintheopticalspec-trum.ThisisconsistentwiththeinterpretationoftheopticalconductivityspectrawiththeΓ(ω)saturation,asdiscussedabove.Thispictureimpliesthattheholedop-ingintoCa2cCuO2Cl2canbedescribedasarigidbandshiftwithoutanylargereconstructionofthevalenceandtheconductionbandintheunderdopedregion.

VII.SUMMARY

Inthispaper,wereporttheresistivityandre ectiv-itymeasurementofCa2 xNaxCuO2Cl2(CNCOC),whichhasapurelytetragonalCuO2planeandthus,isthebestsystemtoinvestigatethechargedynamicsoftetragonallatticewithstrongelectroncorrelation.Itwasfoundthattheabsolutevalueoftheout-of-planeresistivityofCN-COCismuchlargerthanthatofLSCOowingtotheioniccharacterofthe(Ca,Na)Clplane,thoughitstempera-turedependenceissmallerforCNCOC.Thisdiscrepancysuggeststhatthetemperaturedependenceoftheout-of-planeresistivityisdominatedbytheopeningofapseu-dogap.Itwasalsofoundthatthedopingdependenceofthein-planeopticalconductivityspectraofCNCOCissimilarwiththoseofothercupratesuperconductors,butacarefulcomparisonofthespectrabetweenCNCOCandLa2 xSrxCuO4(LSCO)clari esthat(1)thereisasmallpeakaround1.5eVbetweenthecharge-transferpeak(2eV)andaquasi-Drudepeak(below1eV)onlyinLSCO(2)theDrudeweightbelow1eVofCNCOCisalwayslargerthanthatofLSCOatthesamedopinglevel,thoughthesuperconductingtransitiontemperatureislowerforCNCOC.The1.5eVpeakexistingonlyinLSCOcanbeattributedtothechargestripeinLSCO.ThelargerDrudeweightandlowertransitiontempera-tureimpliesthatonlyapartoftheDrudeweightbelow1eVcontributestothesuperconductivity.

Thetemperaturedependenceoftheopticalconductiv-ityspectraofCNCOChasbeenanalyzedbothbythetwo-componentmodel(Drude+Lorentzian)andbytheone-componentmodel(extendedDrudeanalysis).Five ttingparameterscanbeobtainedbythetwo-componentmodel,butthedopingandtemperaturedependenceofthoseparametersarenotingoodagreementwiththetheoreticalpredictions.Ontheotherhand,itwasfoundthattheω-dependenceofΓderivedfromtheextendedDrudeanalysisshowsauniversalchangewithdopingfordi erentsystems.ItwasalsofoundthatΓ(ω)showsasaturationbehaviorabove0.4eV,whichhasthesameoriginoftheresistivitysaturationathightemperatures,

We report the reflectivity and the resistivity measurement of Ca_{2-x}Na_{x}CuO_{2}Cl_{2} (CNCOC), which has a single-CuO2-plane lattice with no orthorhombic distortion. The doping dependence of the in-plane optical conductivity spectra for CNCOC is qualit

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i.e.,kF cannotbesmallerthanunity.Finally,theab-senceofthestructurebelow1.0eVinthepresentopti-calconductivityspectra,togetherwiththeresultoftheARPESmeasurementthatthespectralweightaround(π,0)pointissuppressedbelow0.4eV,suggeststhatonlysmallpocketsexistaround(π/2,π/2)pointintheunderdopedregimeofCNCOC.

Acknowledgments

fuldiscussions,K.TakenakaforsendingushisdataofLSCO,andS.MiyasakaandY.TokurafortheirhelpwiththemeasurementatUV-SOR.Thisworkwaspartlysup-portedbyaGrant-in-AidforThe21stCenturyCOEPro-gram(PhysicsofSelf-organizationSystems)atWasedaUniversityfromtheMinistryofEducation,Sports,Cul-ture,ScienceandTechnologyofJapan

TheauthorswouldliketothankT.Hanagurifortech-nicalassistanceonresistivitymeasurementsandhelp-

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Presentaddress:RISE,WasedaUniversity,Tokyo169-8555,Japan;PRESTO,JapanScienceandTechnologyCorporation,Saitama332-0012,Japan

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