Phase Transition in Anyon Superconductivity at Finite Temper(11)

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,

tobe

A=2+γ1B(3.37)

C1= 3gγ1

γ22

γ2A+

From(3.39)weseethatforT ωctheelectromagnetic eldlong-rangemodepropagatesintothesample,producinganhomogeneousmagneticpenetration.Thisresultisdi erentfromtheoneobtainedinthelow-temperaturelimit(T ωc)[33].InthatlimititwasfoundthatC5=0,whichimpliesthatthelong-rangemodecannotpropagatewithinthesamplewhenauniformandconstantmagnetic eldisperpendicularlyappliedatthesample’sboundaries.

D.InhomogeneousMagneticResponse 2+G)γ2+(gγ11B(3.39)

Asithasbeenpreviouslyestablished,inthehigh-temperaturelimitthecoe cientsA,C1andC5arealldi erentfromzero,i.e.,inthe(T ωc)-phasethemagneticresponseofthechargedanyon uidhasanexponentialdecayingcomponent,aswellas,bothhomogeneousandinhomogeneouspenetrations..Tocompleteourstudyofthemagneticresponseathightemperaturewestillneedtoestimatethecorrespondingvaluesofeachcomponentfortherangeofparametersandtemperatureshereconsidered.

Atthedensitiesunderconsideration,ne m2,theestimatedvaluesofthecoe cientsA,C1andC5inthehigh-temperatureapproximation(T ωc)are

A≈103B,C5≈10 4

λ x(3.41)

B(x)=

where

E0(T)=12√λ x 1(3.42)

2+1

B.Moreover,theinhomogeneousmagnetic eldpenetration(3.42)is

characterizedbyawavelengthλ,whichisproportionaltotheinverseofthelengthscalemagnitude