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1、ATopologicalLookattheQuantumHallEffectTheamazinglyprecisequantizationofHallconductanceinaItturnedoutthatthemagnitude,two-dimensionalelectrongascanbeunderstoodintermsofandeventhesign,oftheHallvoltageatopologicalinvariantknownastheChernnumber.dependsonthematerialpropertiesoftheconductor—the
2、goldleafinHall’sexperiment.ThatmadetheHalleffectJosephE.Avron,DanielOsadchy,andRuediSeileranimportantdiagnostictoolforin-vestigatingthecarriersofelectriccurrent.EventuallyitpointedtothehestoryoftheHalleffectbeginswithamistakemadeconceptofpositivelychargedholesascurrentcarriersinTbyJamesCl
3、erkMaxwell.InthefirsteditionofhisTrea-solids.SoMaxwell,evenwhenhewaswrong,inspiredtiseonElectricityandMagnetism,whichappearedin1873,fruitfulresearch.Maxwelldiscussedthedeflectionofacurrentbyamag-ThequantumHalleffectneticfield.Hethensaid:“Itmustbecarefullyrememberedthatthemechanicalforcewh
4、ichurgesaconductor...acts,Acenturylater,theHalleffectwasrevivedasasourceofnotontheelectriccurrent,butontheconductorwhichcar-astonishingnewphysics.In1980attheGrenobleHighriesit.”Ifreadersarepuzzledbythisassertion,theyMagneticFieldLaboratoryinFrance,KlausvonKlitzingshouldbe.wasstudyingtheHa
5、llconductanceofatwo-dimensionalIn1878,EdwinHall,astudentatJohnsHopkinsUni-electrongasatverylowtemperatures.Hediscovered,inversity,wasreadingMaxwellforaclasstaughtbyHenryessence,thattheHallconductance,asafunctionoftheRowland.HallaskedRowlandaboutMaxwell’sremark.strengthofthemagneticfieldap
6、pliednormaltothegasplane,exhibitedastaircasesequenceofwideplateaus.2Theprofessorrepliedthathe“doubtedthetruthofWithtotallyunanticipatedprecision,thesuccessivevaluesMaxwell’sstatementandhadsometimebeforemadea1oftheHallconductancewereintegermultiplesofafun-hastyexperiment...thoughwithoutsuc
7、cess.”damentalconstantofnature,Hallmadeafreshstartanddesignedadifferentex-e2/h=1/(25812.807572W),periment,aimedatmeasuring,instead,themagneto-resistance—thatis,thechangeoftheelectricalresistanceirrespectiveofthegeometricdetailsoftheexperimentortheduetothemagneticfie
