Phase Transition in Anyon Superconductivity at Finite Temper(12)

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,

AtT ωc,usingthatµ πne

ξ2increaseswiththetemperature(seeeq.(3.22)),wehave,thatthewavelengthdecreases

withT.Thehigh-temperatureleadingbehaviorforλisgivenby

λ≈π1

B,andthetemperature.TheE’sinhomogeneity

alsoincreaseswiththetemperaturethroughλ.

Fromtheobtainedresultsweconcludethatfortemperatureslargerthantheenergygap,thechargedanyon uidisinanewphaseonwhichthesuperconductivityislost(nonMeissnere ectisfoundinthisphase).

Theinductionofinhomogeneouselectricandmagnetic eldswithinthechargedanyon uidathightemperature,indicatesthatsomeredistributionoftheinducedchargeandcurrentsoccursatT ωc.

Toverifythis,letuscalculatetheinducedelectricchargedensityofthechargedmediuminthehigh-temperatureapproximation.Consideringeq.(3.5)inthehigh-temperaturelimit,we ndthattheinducedelectricchargedensitypresentsaninhomogeneousspatialdistributionwithhigh-temperatureleadingcontributiongivenby

√βµeJ0(x)=24Btanhx(3.46)λ

Asdiscussedabove,inthehigh-temperatureregimeλ～

2 Bcosh βµ

2 +1 1 x(3.47)λ

Obviously,thecurrentdensity(3.47)isnotasupercurrentcon nedtothesample’sboundary.

IV.MAGNETICMASSANDRESTENERGYINTHECHARGEDANYONFLUIDATT ωC

Wehaveseenthattheinverselengthscales,ξ1andξ2,arebasicelementsinthedeterminationofthemagneticresponseofthechargedanyon uid.InthisSec.weshallgoonestepforwardinclarifyingthephysicalinterpretationoftheseparameters.Wewillshowthattheinverselengthscales(3.21),(3.22)canbeidenti edwiththemagneticmassesoftheelectromagnetic eldwithinthe uidatT ωc.AparticularlyimportantpointinthisSec.isourproofthattheexistenceathightemperatureofanimaginarymagneticmass(correspondingtotheinverselength(3.22))isnotlinkedtothepresenceoftachyonsinthetheory,ortothebreakingofthelinearapproximation,aswassuggestedinref.[28].Asshownbelow,themagneticmassandtherestenergyarenotthesameintheMCStheory(contrarytowhathappensinaKlein-Gordon-liketheory).

Toinvestigatethemagneticmassesandtherestenergiesassociatedwiththeelectromagneticmodes,weneedtostudytheelectromagnetic elddispersionequation.Withthisaimwestartfromthee ectiveaction(2.18)takeninthecovariantgaugesfortheMaxwellandCS elds

1

α2 µaµ=0(4.1)

α1andα2beingtwoindependentgaugeparameters.

Thecorrespondinge ectiveLagrangiandensityfortheMaxwellandCS eldcon gurationscanberepresentedas

Leff= 1

2 1aµ( k)Dµν(k)aν(k) eAµ( k)Πµν(k)aν(k)(4.2)

1 1wherethematrices µνandDµνaregivenby

12 µν(k)=kgµν 1 1