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1、IntegralquantumHalleffectfornonspecialistsD.R.YennieLaboratoryofNuclearStudies,CornellUniversity,Ithaca,NewYorkf4859InstituteforTheoretica/Physics,UniversityofCalifornia,SantaBarbara,California99108andStanfordLinearAcceleratorCenter,Stanford,California94905Anattemp
2、tismadetodevelopadescriptionofthemultielectronquantumstateresponsiblefortheintegralquantumHalleffect.OnegoalistoprovideintuitivesupportfortheverypowerfulandgeneralargumentofLaughlinthatthetheoreticalrelationshipisinsensitivetocomplicatingdetailsintheinteriorofthesa
3、m-ple.Themodeltheauthorusesissomewhatmorerealisticthanheretoforeinthatitisthreedimensional,doesnotignoretheatomicstructureofthebulkmatter,anddoesnotuseaneffective-massapproximation.Inordertotreattheproblemquantummechanically,thecompletesystem,includingcircuitryexte
4、rnaltothesystemofinterest,isreplacedbyamodelclosedsystemconsistingofafinitenumberofelectrons.Inthismodel,stateswithafiniteHallcurrentandvoltagearemetastableagainstdecaycausedbyinteractionsoutsidethemodel,suchasthosewithbulkmatterexcitations.Suchstatesdescribethetru
5、esituationwellonlyintheconductivityplateaus;betweenplateaus,therewouldbecurrentflowbetweentheHallvoltageprobescorrespondingtodecayingstates.Experimenta'1constraintsreplacethistransversecurrentbyavolt-agedropalongthedirectionofcurrentflow.Theinteractionsbetweentheel
6、ectronsareexpressedintermsofaself-consistentpotentialwhichgivesanindependent-particledescriptionasastartingpoint,andresidu-alinteractionswhicharetreatedbyperturbationtheory.Theself-consistentpotentialisfoundtobeimpor-tantinunderstandingthepropertiesofthequantumstat
7、eofthesystem,suchastheexistenceofthepla-teausinconductivityandhowtheelectronsinthe(effective)two-dimensionalregioncometoequilibriumwiththedifferentFermilevelsinthevoltageprobes.Toallfiniteordersofperturbationtheory,theresidu-alinteractionsarefoundnottoalterthequant
8、izedHallconductivity.CONTENTSAcknowledgments819AppendixA:ApproximateTreatmentoftheWaveFunctionsinTwoDimensions820I.Introduction781AppendixB:Pertu
