Phase Transition in Anyon Superconductivity at Finite Temper(2)

The magnetic response of the charged anyon fluid at temperatures larger than the fermion energy gap is investigated in the self-consistent field approximation. In this temperature region a new phase, characterized by an inhomogeneous magnetic penetration,

authors[27]-[31]haveadvocated

that

the

superconductingphaseevaporatesatany nitetemperature.Inref.[28],ithasbeenindependentlyclaimedthatthedestructionoftheanyonsuperconductingphaseat nitetemperatureisconnectedtotheexistenceofalong-rangemode, 1foundinsidethein nitebulkatT=0.Thislongrangemodeistheconsequenceoftheexistenceofapole～

λ～10 5cmforT～200Kandelectrondensitiescharacteristicofthehigh-Tcsuperconductors).

Ourmainconclusionwasthatthemagneticbehavioroftheanyon uidisnotjustdeterminedbyitsbulkproperties,butitisessentiallya ectedbythesampleboundaryconditions.Theimportanceoftheboundaryconditionsin(2+1)-dimensionalmodelshasbeenpreviouslystressedinref.[34].

Itisnaturaltoexpectthatattemperatureslargerthantheenergygapthissuperconductingbehaviorshouldnotexist.Atthosetemperaturestheelectronthermal uctuationsshouldmakeaccessiblethefreestatesexistingbeyondtheenergygap.Asaconsequence,thechargedanyon uidshouldnotbeaperfectconductoratT ωc.Asignalofsuchatransitionmaybefoundstudyingthesystemmagneticresponseatthosetemperatures.Themaingoalinthispaperistoinvestigatethecharacteristicsofthemagneticresponseinthishightemperaturephase.

InwhatfollowsweshowthatatT ωcanexternallyappliedconstantandhomogeneousmagnetic eldcanpenetratethesample,givingrisetoaperiodicinhomogeneousmagnetic eldwithinthebulk.Theinhomogeneityofthemagneticresponseincreaseswiththetemperature.Wealso ndthat,contrarytotheT ωccase,along-rangepenetration,associatedtoamasslessmodeoftheelectromagnetic eldwithintheanyon uid,canpenetratetheboundedsampleinthehightemperaturephase.Nevertheless,intherangeoftemperaturesconsideredthee ectofthishomogeneous eldpenetrationisnegligibleascomparedtotheinhomogeneouscomponent.

Theseresultscorroboratetheexistenceofaphasetransitioninthechargedanyon uidfromasuperconductingphase,atT ωc(seeRef.[33]),toanon-superconductingphase,atT ωc.Theinhomogeneouscharacterofthemagneticresponseinthehightemperaturephaseislinkedtotheinhomogeneityofthespatialdistributionoftheinducedmany-particlechargeandcurrentdensitiesatT ωc.

Wealsoprovethattheinhomogeneousmagneticpenetrationisassociatedtoanimaginarymagneticmassassociatedtooneoftheelectromagnetic eldmodeswithinthechargedanyon uid.TheappearanceofanimaginarymagneticmassatT ωcbynomeansindicatesthatthelinearapproximationusedinthesecalculationsisbrokenbythepresenceoftachyons.Tachyons,asitisknown,correspondtoimaginaryrest-energysolutions.TherestenergyandthemagneticmassspectrumoftheMCStheoryat nitedensityarenotthesameatT ωc,asprovedinSec.4.FortheMCStheoryat nitedensity,weshowthattherestenergiesoftheelectromagnetic eldmodesatT ωcarereal.

Theplanforthepaperisasfollows.InSec.2,forcompleteness,aswellasfortheconvenienceofthereader,wereviewthemany-particle(2+1)-dimensionalMCSmodelusedtodescribethechargedanyon uidintheself-consistent eldapproximation.Principalattentionisgiventothederivationofthehigh-temperatureMCSe ectiveactioninthelinearapproximation.InSec.3westudythemagneticresponseintheself-consistent eldapproximationofachargedanyon uidcon nedtoahalfplaneinthe(T ωc)-phase.We ndtheanalyticalsolutionoftheMCS eldequationsthatsatis esthecorrespondingboundaryconditionsandminimizesthesystemfreeenergy.Thepropagationmodesofthemagnetic eldwithintheanyon uidhavethreecontributions:onethatdecaysexponentiallyinspace,otherthataccountsforanhomogeneous eldpenetration,andathirdthatchangesperiodicallyinspacewithinthesample.Whenallthecoe cientsappearinginthemagnetic eldsolutionareevaluatedfortherangeoftemperaturesandothercharacteristicparametervalues,we ndthattheleadingterminthemagneticresponseisaninhomogeneousmagnetic eldwithacharacteristicwavelengththatdecreaseswiththetemperature.InSec.4weinvestigatethedispersionequationfortheMaxwell eldinthehigh-temperatureapproximation.WesolvethisequationinarbitrarycovariantgaugesfortheMaxwellandCS eldstoobtainthemagneticmassesofthechargedanyon uidinthehigh-temperaturephase.Asexpected,themagneticmassesturnouttobeequaltotheinverselengthscaleswhichcharacterizethemagneticresponseoftheanyon uidinthisphase.Wethenprovethattheexistenceofanimaginarymagneticmasscannotbeassociatedtoatachyonicmodeinthismany-particlesystemwithCSinteractions.Indoingthat,we ndtherestenergiesoftheelectromagnetic eldmodesatT ωc.Sec.6containsthesummaryanddiscussion.