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1、TopologicalinsulatorsandsuperconductorsXiao-LiangQi1,2andShou-ChengZhang21MicrosoftResearch,StationQ,ElingsHall,UniversityofCalifornia,SantaBarbara,CA93106,USA2DepartmentofPhysics,StanfordUniversity,Stanford,CA94305Topologicalinsulatorsarenewstatesofquantummatterwhichcannotbeadiabaticall
2、yconnectedtoconventionalinsulatorsandsemiconductors.Theyarecharacterizedbyafullinsulatinggapinthebulkandgaplessedgeorsurfacestateswhichareprotectedbytime-reversalsymmetry.Thesetopologi-calmaterialshavebeentheoreticallypredictedandexperimentallyobservedinavarietyofsystems,includingHgTequa
3、ntumwells,BiSballoys,andBi2Te3andBi2Se3crystals.Wereviewtheoreti-calmodels,materialspropertiesandexperimentalresultsontwo-dimensionalandthree-dimensionaltopologicalinsulators,anddiscussboththetopologicalbandtheoryandthetopologicalfieldtheory.Topologicalsuperconductorshaveafullpairinggapin
4、thebulkandgaplesssurfacestatesconsistingofMajoranafermions.Wereviewthetheoryoftopologicalsuperconductorsincloseanalogytothetheoryoftopologicalinsulators.PACSnumbers:73.20.-r,73.43.-f,85.75.-d,74.90.+nCONTENTSA.Topologicalfieldtheory351.Chern-Simonsinsulatorin2+1dimensions35I.Introduction1
5、2.Chern-Simonsinsulatorin4+1dimensions353.Dimensionalreductiontothethree-dimensionalZ2II.Two-DimensionalTopologicalInsulators4topologicalinsulator36A.Effectivemodelofthetwo-dimensionaltime-reversalinvariant4.Furtherdimensionalreductiontothetwo-dimensionalZ2topologicalinsulatorinHgTe/CdTe
6、quantumwells5topologicalinsulator39B.Explicitsolutionofthehelicaledgestates75.GeneralphasediagramoftopologicalMottinsulatorandC.Physicalpropertiesofthehelicaledgestates8topologicalAndersoninsulator391.Topologicalprotectionofthehelicaledgestates8B.Topologicalbandtheory402.Interactionsandq
7、uencheddisorder10C.Reductionfromtopologicalfieldtheorytotopologicalband3.Helicaledgestatesandtheholographicprinciple10theory424.Transporttheoryofthehelicaledgestates11V.TopologicalSuperconductorsandSuperfluids42D.Topologicalexcitations12A.Effectivemodelsoftime-reversalinvar
