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1、PHYSICALREVIEWB76,0453022007TopologicalinsulatorswithinversionsymmetryLiangFuandC.L.KaneDepartmentofPhysicsandAstronomy,UniversityofPennsylvania,Philadelphia,Pennsylvania19104,USAReceived14November2006;revisedmanuscriptreceived17January2007;published2July2007Topologicalinsulatorsarematerialswith
2、abulkexcitationgapgeneratedbythespin-orbitinteractionthataredifferentfromconventionalinsulators.ThisdistinctionischaracterizedbyZ2topologicalinvariants,whichcharacterizethegroundstate.Intwodimensions,thereisasingleZ2invariantthatdistinguishestheordinaryinsulatorfromthequantumspin-Hallphase.Inthreedi
3、mensions,therearefourZ2invariantsthatdistinguishtheordinaryinsulatorfromweakandstrongtopologicalinsulators.Thesephasesarecharacterizedbythepresenceofgaplesssurfaceoredgestates.Inthetwo-dimensionalquantumspin-Hallphaseandthethree-dimensionalstrongtopologicalinsulator,thesestatesarerobustandareinsen
4、sitivetoweakdisorderandinteractions.Inthispaper,weshowthatthepresenceofinversionsymmetrygreatlysimplifiestheproblemofevaluatingtheZ2invariants.WeshowthattheinvariantscanbedeterminedfromtheknowledgeoftheparityoftheoccupiedBlochwavefunctionsatthetime-reversalinvariantpointsintheBrillouinzone.Usingthisa
5、pproach,wepredictanumberofspecificmaterialsthatarestrongtopologicalinsulators,includingthesemiconductingalloyBi1−xSbxaswellas-SnandHgTeunderuniaxialstrain.Thispaperalsoincludesanexpandeddiscussionofourformulationofthetopologicalinsulatorsinbothtwoandthreedimensions,aswellasimplicationsforexperiments
6、.DOI:10.1103/PhysRevB.76.045302PACSnumbers:73.43.f,72.25.Hg,73.20.r,85.75.dI.INTRODUCTIONIQHEphases,whichisintimatelyrelatedtotheirtopology,istheexistenceofgaplesschiraledgestateswhicharerobustinInelementarysolid-statephysicstextbooks,aninsulatoristhepresenceofdisorder.7,8describedasamaterialwi
7、thanenergygapseparatingfilledRecently,newtopologicalinsulatingphasesforsystemsandemptyenergybands.Amoresophisticateddefinitionofwithtime-reversalsymmetryhavebeendiscovered.915Inaninsulatoristhatofamater
