Phase Transition in Anyon Superconductivity at Finite Temper(14)

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,

A.Electromagnetic eldmagneticmassesathightemperatures

To ndtheelectromagnetic eldmagneticmasseswemustsolvethedispersionequation(4.8)atω=0.Sinceweareinterestedinthemagneticmassesattemperatureshigherthantheenergygap(T ωc),weshouldconsiderinsolving(4.8)thepolarizationoperatorcoe cientsinthehigh-temperatureapproximation(2.38).

Letusdetermine rsttheexpressionofthematrixNµν(k)(eq.(4.7))atω=0.InthiscasethematrixDλρ(k)appearingineq.(4.7)takestheform

Dλρ(k)=k2

π+Π1(4.16)

Thus,aftertakingthematrixproductsindicatedin(4.7)withthepolarizationoperator(4.5)evaluatedatω=0,we nd,

Nµν(k)=e2

α1

with 2k+e2A1G1k21+e2G1Π2+e4G22=0

G1=B(4.19)

α2D+Π1(4.21)

ForN=2,takingintoaccountthatinnaturalunitse2～105cm 1,andconsideringthecharacteristicvaluesne=2×1014cm 2andme=2.6×1010cm 1,wecanestimatetherelativeordersbetweenthepolarizationoperatorcoe cients(2.38)attemperatureslargerthanωcas

Π0≈ 108e2Π1≈ 107e4Π0′≈1020e4Π2

is

det[ (k) N(k)] (Π2Π0′)2(4.22)Takingintoaccounttherelations(4.22),thehigh-temperatureleadingcontributiontothedispersionequation(4.19)