Topological insulators and the dirac equation.pdf

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1、SPINVol.1,No.1(2011)33
44©WorldScientificPublishingCompanyDOI:10.1142/S2010324711000057TOPOLOGICALINSULATORANDTHEDIRACEQUATIONSHUN-QINGSHEN*,WEN-YUSHANandHAI-ZHOULUDepartmentofPhysicsandCenterforTheoreticalandComputationalPhysicsTheUniversityofHongKong,PokfulamRoad,HongKong,P.R.China*

2、sshen@hkucc.hku.hkReceived7April2011Accepted22May2011WepresentageneraldescriptionoftopologicalinsulatorsfromthepointofviewofDiracequations.TheZ2indexfortheDiracequationisalwayszero,andthustheDiracequationistopologicallytrivial.Afterthequadraticterminmomentumisintroducedtocorrectthema

3、sstermmorthebandgapoftheDiracequation,i.e.,m!m
Bp2,theZ2indexismodifiedas1formB>0and0formB<0.ForafixedBthereexistsatopologicalquantumphasetransitionfromatopologicallytrivialsystemtoanontrivialsystemwhenthesignofmassmchanges.AseriesofsolutionsneartheboundaryinthemodifiedDiracequationisob

4、tained,whichischaracteristicoftopologicalinsulator.FromthesolutionsoftheboundstatesandtheZ2indexweestablisharelationbetweentheDiracequationandtopologicalinsulators.Keywords:Spintronics;topologicalinsulator;Diracequation.1.IntroductionexperimentallyintegerquantumHalleffect(IQHE)SPIN201

5、1.01:33-44.Downloadedfromwww.worldscientific.comintwo-dimensional(2D)electrongasinsemi-Translationalinvarianceincrystallatticesandtheconductorheterojunctioninastrongmagneticfield,Blochtheoremforthewavefunctionofelectronsininwhichlongitudinalconductancebecomeszerosolidsmakesitpossiblef

6、orustoknowthebandbyNANJINGUNIVERSITY-LIBRARYLIBRARYon12/03/12.Forpersonaluseonly.whilethequantumplateauoftheHallconductancestructuresofsolidandwhyasolidismetal,insu-25appearsate=h(isaninteger).Twoyearslater,latororsemiconductor.InrecentyearsithasbeenTsuietal.observedthefractionalqu

7、antumHallfoundthatanewclassofmaterialspossessesaeffect(FQHE)inasamplewithhighermobility.6InfeaturethatitsbulkisinsulatingwhileitssurfaceorthetheoryofedgestatesforIQHE,electronsformedgeismetallic.ThismetallicbehaviorisquitediscreteLandaulevelsinastrongmagneticfield.robustagainstimpuriti

8、esorinteract