Charge and Statistics of Quasiholes in Pfaffian States of Composite Fermion Excitations

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1、ChargeandStatisticsofQuasiholesinPfaffianStatesofCompositeFermionExcitationsPiotrSitkoInstituteofPhysics,WroclawUniversityofTechnology,Wybrze˙zeWyspia´nskiego27,50-370Wroclaw,Poland.AbstractThechargeofquasiparticlesinPfaffianstatesofcompositefermionexcita-tions(thepresenceofw

2、hichisindicatedbyrecentexperiments)isfound.AtthefillingfractionofthePfaffianstateν=p/q(ofthelowestLandaulevel)thechargeis±e/(2q).AsinthecaseofthePfaffianstateofelectronsthestatisticsofNqhquasiholesinthePfaffianstatecorrespondstothespinorrepresentationofU(1)×SO(2Nqh)(thecontinuou

3、sextensionofthebraidi(1+1)πgroup).HereU(1)isgivenbythephasefactore84mwithm=1+α,α–theexclusionstatisticsparameterofJainquasiparticles.ThepossiblityofRead-RezayistatesofJainquasiparticlesisalsodiscussed.arXiv:cond-mat/0402653v2[cond-mat.mes-hall]25Mar2004TypesetusingREVTEX1

4、Recently,thenon-Laughlinandnon-JainstateswereobservedinthefractionalquantumHalleffect[1].Theycanbeinterpretedascondensedstatesofcompositefermionexcitations[2,3].Even-denominatorstates(i.e.atfillingfractionswithanevendenominator)canbeseenasPfaffianstatesofJainquasiparticles.Od

5、d-denominatorstatescorrespondtothecondensedstatesofcompositefermionexcitationswhichcaneitherbeLaughlin[4](orJain)statesorcondensedstatesofdifferentorigin.Onepossiblity(ascompetingtoLaughlin-Jainstates)istheclassofstatesproposedbyReadandRezayi[5]forelectronstatesinhigherLan

6、daulevels(Read-Rezayistatesresultfromclusteringofanumberofparticles,thePfaffianstateisthestateofpairsofparticles[6]).Theotherproposedstatesfortheoriginofodd-denominatorstatesareHalperinpairedstates[7–9].Thecompositefermionapproachpredictstheso-calledJainstatesatfillingfracti

7、onsofn0theformν=2p0n0+β0(where2p0–theChern-Simonscompositefermionparameterbeinganevennumber,n0–thenumberofeffectiveshellsfilled,β0–thesignoftheeffectivefieldwithrespecttotheexternalmagneticfield).TheeffectivefieldisfoundwhenthemeanChern-Simonscompositefermionfieldisaddedtotheexte

8、rnalmagneticfield.Letusintroducethecondensedstatesofcompositefermionexcitations(following[2])whic