Phase Transition in Anyon Superconductivity at Finite Temper

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,

PHASETRANSITIONINANYONSUPERCONDUCTIVITYATFINITE

TEMPERATURE

E.J.Ferrer andV.delaIncera

Dept.ofPhysics,StateUniversityofNewYork,Fredonia,NY14063,USA

(SUNY-FRE-98-04)

Themagneticresponseofthechargedanyon uidattemperatureslargerthanthefermionenery

gap(T ωc)isinvestigatedintheself-consistent eldapproximation.Inthistemperatureregiona

newphase,characterizedbyaninhomogeneousmagneticpenetration,isfound.Theinhomogeneity

islinkedtotheexistenceofanimaginarymagneticmasswhichincreaseswiththetemperatureat

T ωc.Thesystemstabilityinthe(T ωc)-phaseisprovedbyinvestigatingtheelectromagnetic

eldrest-energyspectrum.

arXiv:hep-th/9805039v1 7 May 1998I.INTRODUCTIONInrecentyearstherehasbeenmuchinterestininvestigating(2+1)-dimensionalgaugetheorieswithChern-Simons(CS)interactions.Thisinterestisdue,inpart,toavarietyofsigni cantphysicalapplicationsofthesetheoriesinQFT,aswellasincondensedmatterphysics.AwellknownexampleinQFTistheDeser,JackiwandTempletonParityAnomaly[1].Thisresultshowsthatthe uctuationsofamassiveFermi eldinducesaCSterminthee ectiveactionofthegauge elds.Inthiscontextthephotonacquiresatopologicalmass[1],[2].Parityviolation[3]andvortexsolutionsinlowerdimensions[4]areamongtheconsequencesofthepresenceofCSterms.Ontheotherhand,ithasbeenshownthatwhenDiracfermionsarecoupledtoaMaxwell-Chern-Simons(MCS)gauge eld,theLorentzsymmetrycanbespontaneouslybrokenbythedynamicalgenerationofamagnetic eld[5].Thee ectsofCStermsinsupersymmetricmodelshavebeenalsoinvestigated[6].Incondensedmatter,CSmodelshavebeenconsideredinthestudyofdi erentphysicalapplications.CStheoriesinvolvingseveralvectorpotentialsareknowntobeparticularlyappropriatefordescribingthequantumHalle ect[7],[8],[9].ArecentmodelofthefractionalquantumHalle ectconsidersthattheelectronsaretransformedintocompositefermionsbyattachingtwoarti cialstatistical uxquantatoeachelectron[10].Thegauge eldtheorydescribingthesecompositefermionsintroducesthestatisticalgauge uxviaCS elds[11].Whenmatter eldiscoupledtotheCSgauge eldsin(2+1)-dimensions,asuitabledescriptionforanyonsisobtained[12],[13].Anyons[14],[15]areparticleswithfractionalstatisticsin(2+1)-dimensions.TheanyondescriptionwithintheCSgaugetheoryisequivalenttoattaching uxtubestothechargedfermions.TheAharonov-Bohmphasesresultingfromtheadiabatictransportoftwoanyonsisthesourceofthefractionalexchangestatistics[15].Ithasbeenarguedthatstronglycorrelatedelectronsystemsintwodimensionscanbedescribedbyane ective eldtheoryofanyons[16],[17].Anyonscanbealsoobtainedassolitonswhichfractionalspininelectronsystems.Excitationswithfractionalspinintwodimensionalsystemsnecessarilyobeyfractionalstatistics[18].Animportant

featureoftheanyontheoryisthatitviolatesparityandtime-reversalinvariances.Althoughthereareclaimsthatanyonscouldplayabasicroleinhigh-TCsuperconductivity[17]-[20],atpresentnoexperimentalevidencesofPandTviolationinhigh-TCsuperconductivityhavebeencon rmed.Itshouldbepointedout,nevertheless,thatitispossibletoconstructmoresophisticatedPandTinvariantanyonicmodels[21].

Whetherlinkedornottohigh-TCsuperconductivity,anyonsuperconductivityisaninterestinge ectinitsownright,anddeservesadeeperstudy.Asitisknown,anyonsuperconductivityhasanorigindi erentfromtheNambu-Goldstone-Higgslikemechanism.Thegenesisoftheanyonsuperconductivityisgivenbythespontaneouslyviolationofcommutativityoftranslationsinthefreeanyonsystem[22].Thisnewmechanismmayhavewiderapplicationsthantheoriginalphysicalproblemthatmotivateditsstudy.

ThesuperconductingbehaviorofanyonsystemsatT=0hasbeeninvestigatedbymanyauthors[13],[19]-[25].AtT=0,anyonsuperconductivityappearsduetotheexactcancellationbetweenthebareandinducedCStermsinthee ectiveactionofthetheory[26].However,atT=0thiscancelationdoesnottakeplace[27].Hence,several