THE WEAK-TO-STRONG COUPLING PHENOMENA IN HIGH-TEMPERATURE SUPERCONDUCTIVITY

Abstract

The periodofconventionalsuperconductivitybeganin1911withKammerlingh Onnes’sdiscoveryofsuperconductivity.Incontrast,theeraofhigh-temperature superconductivity(HTSC)commencedin1986withBednorzandMüller’sbreak- through findingofthehigh-temperaturesuperconductor(HTS)La2−xSrxCuO4 with the transitiontemperature(Tc) of 37.5 K. Thisphenomenonbecameoneofthemost exciting andintriguingfieldsofcondensedmatterphysicsduetohistoriclandmarks. In thelastcentury,plentyofexperimentalandtheoreticalinvestigationshavebeen carried outtounderstandthemechanismandcharacteristicsofsuperconductorsin a bettermannerandthehuntisstillgoingon.Therearetwomajorturningpoints in thetheoreticalunderstandingofconventionalsuperconductivity,namely:(i)the phenomenologicaltheoryofsuperconductivitydevelopedbyGinzburgandLandau, knownastheGinzburg-Landau(GL)theory,and(ii)themicroscopictheoryofsu- perconductivity,developedbyBardeen,Cooper,andSchrieffer, knownastheBCS theory. BaskaranandAnderson’sgaugetheoryofHTSandAnderson’sresonatingvalance bondtheory(RVB)ofHTSforstronglycorrelatedFermisystemsareworthmen- tioning amongthenumerousmodelspresentedtoexplaintheHTSC.Moriyaetal. andVarmainvestigatedthesignificanceofantiferromagneticspinfluctuationsinthe occurrenceofHTSC.OftheseveralproposedmechanismsofHTSC,thephononis alwaysthoughttobeoneoftheentitiesthathelpinformingthesuperconducting pairs, e.g.throughthedressingofelectronswithphononsintheformofpolarons, bipolarons,andsoon. The understandingofseveralunusualpropertiesofHTS,namely:anisotropyof superconductinggap(SG),thehighvalue(5to8)of 2!/kBTc, dx2−y2 pairingsym- metry,etc.havebecomeachallengefortheorists.TheBCStheorycouldnot explain theseunexpectedfeatures,forcingthephysiciststolookoutsidethebox.To understand themechanismofHTSCincupratesuperconductors,Fujitaetal.bor- rowedtheideaofattractivepotentialbetweentwoelectronsfromtheBCStheory. They showedthe d-waveCooper-pair(pairon)formationinthecopper-oxideplane. Though themechanismofHTSCisnotfullyknown,theelectron-phononinteraction hasemergedasacriticalaspectinthetheoreticaldevelopmentofbothconventional and HTSCsuperconductivity.Also,athoroughresearchonanharmonicityischal- lengingsinceanharmonicdisturbancesaresignificantevenatverylowtemperatures. Furthermore,theeffects ofimpurities,thathavebeenwellexploredinsolids,also playanimportantroleincomprehendingtheproblemofHTSCinabroadercontext. As aresult,asimultaneousandprecisetreatmentoftheimpactofbothanharmonic- ityandimpurities,eventhoughcomplex,yetisnecessary.Thisdissertationisan efforttowardsathoroughtheoreticalapproachforcomprehendingtheunderlying physicsofthephenomenonofHTSC.Thefollowingistheframeworkofthisthesis: ChapterI describesabriefoverviewofthehistoricaladvancementsinconventional andhigh-temperaturesuperconductivity.Intheend,themotivationandstateof the art-“methodology”forthepresentresearchworkhavebeenpresentedbrieflyto explain theoutlayofthethesis. ChapterII is devotedtothedevelopmentofpaironGreen’sfunctionwiththehelp of quantumdynamicalmany-bodyproblemviaaHamiltonianthatencompassesthe contributionofpairons,pairon-phononinteractions,anharmonicities,anddefects. Hence aGreen’sfunctionhasbeendevelopedforpairons.Therafter,therenor- malized andperturbedmodepairondispersion,energylinewidthandshift,den- sityofstatesandsuperconductinggapequationhavebeenderivedandsuccessfully analyzed forrepresentativecuprateHTSYBa2Cu3O7−!. Therenormalizedpairon dispersionexhibitstheinfluenceofdefectsandanharmonicitiesandprovidesinfor- mationaboutthepaironexcitationsneartheFermisurface.Further,theanisotropy of superconductinggapandpairingsymmetryhavebeenanalyzedusingtherenor- malizedpairondispersionplotforYBa2Cu3O7−!. Thedevelopedgapequation,a function oftemperature,Fermienergy,andrenormalizedpaironenergy,hasbeen discussed. ChapterIII facilitates thedevelopmentofamicroscopictheorybyconsideringa Hamiltonian whichconsistsofelectroncontribution,phononcontribution,theeffect of linearcouplingbetweenelectronsandphonons,ofanharmonicitiesanddefects. This Hamiltoniansuccessfullyexplainsthespectacularbehaviorofthevarioussuper- conducting propertiesinhigh-temperaturesuperconductors.TheGreen’sfunction for polaronsandphononshavebeenderivedseparately,followedbythederivation of renormalizedenergies,energylinewidths,andshifts,thedensityofstates,en- ergy,heatcapacity,andsuperconductinggapequation.TheYBa2Cu3O7−! cuprate hasbeenhiredfornumericalanalysis.Anexcellentagreementhasbeenobtained betweentheevaluatedandexperimentalresults. ChapterIV is dedicatedtothedevelopmentoftheexpressionforelectron-phonon coupling coefficient(gk). InthetheoreticaldevelopmentofHTSC,electron-phonon coupling stronglyinfluencestheelectrondynamics,andmustthereforebeincludedin anymicroscopictheoryofsuperconductivity.Also,itprovidesthenaturalsourcefor the d-wavepairinginHTScuprates.Here,theexpressionforgk hasbeenobtainedby solving asixth-orderpolynomialequationdevelopedviaquantumdynamicalmany- bodytheoryofelectronandphononGreen’sfunctionsforhigh-temperaturesuper- conductors. Theobtainedexpressionforgk dependsonthetemperature,electron-, phonon-,andpairon-frequencyanddistributionfunctionsofelectrons,phonons,and pairons. Theobtainedgk wasfurtheremployedtoevaluatethesuperconductinggap via BCS-andMcMillan-gapequations.Thevariationofgk with wavevectorand temperaturehasalsobeenstudied. ChapterV offers anewapproachtothepotentialenergyofthesolids.Inthis,an expression hasbeenobtainedfortheinteractionenergyasafunctionofinter-atomic separation. Next,asanewconcept,weconsiderthepotentialenergyasafunction of volumeinsteadofinter-atomicseparationofsolidsusingsimplethermodynamical approachwithoutusinganyempiricalresults.Thisapproachisappropriatetothe study ofthesystemshavinglargenumberofatomsperunitcell.Tocheckthevalidity of themodel,thephonondensityofstatesforhigh-temperaturesuperconductors YBa2Cu3O7−! andLa2−xSrxCuO4 hasbeenobtained.Further,acomparisonofthe obtained resultswiththeavailableexperimentaldataandwiththeearliertheoretical workhasbeenpresented.Fromtheresultsitcanbespeculatedthatthephonon densityofstatesevaluatedwiththehelpoftheproposedmodelisshowingafar betteragreementwiththeexperimentalcurvethanthoseevaluatedintheearlier works. ChapterVI summaries allthekeyfindingsandconclusionsobtainedinthisdis- sertation andattheend,theoutlineoffutureworkhasbeenlisted.