Phase Transition in Anyon Superconductivity at Finite Temper(17)

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,

V.CONCLUDINGREMARKS

Theparticleenergyspectrumoftheanyontheoryexhibitsabandstructuregivenbydi erentLandaulevelsseparatedbyanenergygapωc.TheenergygapisproportionaltothebackgroundCSmagnetic eld

bwhatdeterminestheenergygap

(ωc=

Tinitshigh-

temperatureleadingorder.Thatis,thespatialinhomogeneityofthemany-particlemagneticresponsewillincreasewiththetemperatureinthisnewphase.

TheabsenceoftheMeissnere ectatT ωcisrelatedtotheappearingofanimaginarymagneticmassM3inthisphase(eq.(4.33)).Theexistenceofanimaginarymagneticmasscannotbeassociatedwithatachyonicmodeinthismany-particlesystemwithCSinteractions.Thereasonisthatthemagneticmassesandtherestenergiesoftheelectromagnetic eldmodesarenotthesamewithinthechargedanyon uid.

Itisimportanttonotethatinobtainingtheinhomogeneousmagneticresponseathightemperatures,itwascrucialthatthepolarizationoperatorcoe cientΠ0′changeditssignfromapositivevalueatT ωc[28],[31],[33],toanegativevalueatT ωc(eq.(2.38)).Thatis,becauseΠ0′changesitssign,whileΠ2continuespositive,wehavethatM3isimaginaryineq.(4.33).

Finally,weshouldstatethattheresultsobtainedinRef.[33]andinthispaperforthesuperconductingpropertiesofthechargedanyon uidhavebeenderivedonthebaseofalinearapproximation.Ifnonlineare ects,asforinstancevortices,areconsidered,itispossiblethataricherscenarioforthesuperconductingphasesoftheanyonsystemwillappear.

Acknowledgments

ThisresearchhasbeensupportedinpartbytheNationalScienceFoundationunderGrantNo.PHY-9722059.