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1、INSIGHT PERSPECTIVENATURE
2、Vol464
3、11March2010
4、doi:10.1038/nature08916Thebirthoftopologicalinsulators1,2JoelE.MooreCertaininsulatorshaveexoticmetallicstatesontheirsurfaces.Thesestatesareformedbytopologicaleffectsthatalsorendertheelectronstravellingonsuchsurfacesinsensitivetoscatteringbyimp
5、urities.Suchtopologicalinsulatorsmayprovidenewroutestogeneratingnovelphasesandparticles,possiblyfindingusesintechnologicalapplicationsinspintronicsandquantumcomputing.Manyaspectsofcondensed-matterphysicsareconcernedwithtwisted,withoutbeingcut.Nevertheless,theseinvariantsdochangeunderstan
6、dinghoworderemergeswhenaverylargenumberofsimpleincrossingtheinterfacebetweentopologicalandordinaryinsulators,constituents,suchasions,magneticmomentsorelectrons,interactwithsobycontradictionthesurfacecannotremaininsulating,whichiseachother.Inorderedphasessuchascrystalsandmagnets,theorderi
7、sanalogoustocuttingtheknot.describedthroughsymmetrybreaking:inacrystal,ionsarearrangedInatopologicalinsulator,thecomponentthatis‘knotted’istheperiodicallyowingtotheirelectrostaticinteractions,therebybreakingelectron’swavefunctionasitmovesthroughmomentumspace.Associ-thecontinuoussymmetryo
8、fspaceunderrotationsandtranslations;atedwiththisknottingaretopologicalinvariants(usuallyexpressedasintypicalmagnets,someoftherotationalsymmetryofspinspaceisintegralsinvolvingthewavefunction)thatcannotchangeaslongasthebroken,togetherwiththetime-reversalsymmetry.materialremainsinsulating.E
9、venwhentheboundarybetweenordi-Amajordiscoveryinthe1980swasthatelectronsthatareconfinednaryinsulatorsandtopologicalinsulatorsisatomicallysharpandthetotwodimensionsandsubjecttoastrongmagneticfieldshowacom-continuousdescriptionusingtopologymightnotseemtobeapplica-pletelydifferent,topologica
10、l,typeoforder,whichunderliesthequantumble,thereareneverthelessmetallicdelocalizedwavefunctionsatthisHalleffect.Consequencesofthisorderincludedissipationlesstransportboundary.InFig.1b,thesimplestcaseofknottingina3Delectronicandemergentparticleswithfractionalchargeandstatis
