拓扑绝缘体及其研究进展

http:(2010)8*叶飞1苏刚2,(1100049)(2100049).,.,:,.,..,,,TopologicalinsulatorsYEFei1SUGang2,(1CollegeofMaterialsScienceandOptoelectronicTechnology,GraduatedUniversityofChineseAcademyofSciences,Beijing100049,China)(2CollegeofPhysicalSciences,GraduatedUniversityofChineseAcademyofSciences,Beijing100049,China)AbstractAnewkindofinsulatorhasbeenproposedrecently,whichisfullygappedinthebulkbuthasametallicedgeorsurfacestatesthatareprotectedtopologically.Theseelectronicmaterialsaredubbedastopologicalinsulators(TIs).Generallyspeaking,TIscanbedividedintotwoclasses.OneisthequantumHallsystemwhichwasfoundinthe1980stoshowbreakingoftimereversalsymmetry(TRS),andanotheristhenewlydiscoveredtypewhichdoesnotdemonstrateTRSbreakingandhasat-tractedmuchattentionrecently.ThisarticlepresentsabriefreviewofrecentadvancesinthedevelopmentofTIs.Keywordstopologicalinsulator,quantumHalleffect,quantumspinHalleffect,topologicalclassification*(:10904081)2010-05-10.Email:[e-mail]1),,1引言,.(1(a)),,.,,.,,,.(1(b)),.,.,.1),.56439(2010)8http:(),,.,..,.,.,,,.,,(1(c)(d)).,.,.1.(a),(b),(c),(d).,,,.,((c)(d)),2整数量子霍尔系统80.,e2/h,10-8[1]..,,.,,,.,(2(a)),[2,3].,.,80,,,[4]..,|un(k):H(k)|un(k)=En(k)|un(k),(1)n,k.N.|un(k),()A=iNn=1un(k)|k|un(k),,F=kA.,U(1),ei(k)|un(k)(1).,|un(k),|un(k)ein(k)|un(k),,A(k)A(k)-kNn=1n(k),F.AF,.,,[5].,,nw,12d2kF(k)=nw.(2),nw=12Adl,.,nw,,.,H(k),nw.,nw.1982,Thouless(TKN2)[6],H,nwe2/h.,..,(nw0)(nw=0,),,nw,565http:(2010)8,nw.,,(2(a)).,.nw.2:(a);(b),,,,.1988,Haldane[7].,,,.,H(h)(k)=h(k)s,(3)s22,,h(k).,H=ne2/h.h^h/|h|,nn=14d2k(kxh^kyh^)h^.(4)h(k)S2,n((4))[8].Haldane,hZKK*.,n=1,.,Haldane1(c),2(a).3二维自旋霍尔绝缘体,Ha-ldane,,,nw.1983,TKN2nw[9].,nw=0,,,jx=HEy.,.,=exp(iU^y),,U^yy.,2=1.,2=-1,Kramers,,SU(2).Dyson1962,[10].1988,Avron[11],,.3/2,.2001,[12],,U(1)SU(2).,.,SU(2).,Murakami[13].2005,KaneMele,,Sz[14].,:H(k)=Hh(k)00Hh(k),(5)Hh,(k)()Haldane.[15].,H(k)-1=H(-k).,H=e2hH=-e2h,cH=0;sH=12(h-h)=e2h.56639(2010)8http:(1(d)2(b)).x,y,ky=0ky=,.,,.[16],,.,V=V,(,V)=-(V,),(,V)=0,.SZ,Rashba,SZ,.KaneMele,,[17],,helicalliquid[18].Z2,.,,,.,,,..,.,10-3meV[15],.,.2006,Bernevig,Hughes,HgTeCdTe[19].,s,p,CdTe.HgTe,,s-p.,.CdTe-HgTe-CdTe,HgTe,.,,InAs/GaSb[20].2007,CdTe-HgTe-CdTe,d.,HgTedc.ddc,0,,CdTe.ddc,2e2h,.,,HgTe,..,.,[21,22],.4三维拓扑绝缘体2006,3[2325].,[12][26].,,4.,,Kramers,.,Z2,.FuKane,,[27].mn(k)um(k)||un(-k).,8,(=1,,8),,k-k,3(a).,Tmn()=-mn(),,567http:(2010)83(a),;(b),Pfaffian.=pf[()]/det[()],1.,0:(-1)0=8=1.(6),,|un(k),,,.,31,2,3,4.0=1,;0=01,2,3,,,.FuKane,,,m()=1,=2Nm=1m(),2N..FuKaneBi1-xSbx-Sn.2008,HsiehBi1-xSbx,[28].,.2009,Bi2Te3,Bi2Se3,,[29].,PrincetonBi2Te3Bi2Se3,[30].,Bi2Se30.3eV,.,Bi2Se3Bi1-xSbx,,,.,,Bi2Se3Bi2Te3[31,32],.SrTiO3Bi2Se3[33],.,TlBiQ2TlSbQ2[34](QTe,SeS).,[29]Hsurface=-iF()z,(7)F,..k,3(b).,2,.,k-k,,[35].,.,,,,.,,RKKY[3638].,,[39].,Fermiondoubling.,80,,[40].,,,,.,,,[41].5拓扑绝缘体有效场论,-[42],.,Huges56839(2010)8http:[26],4+1.,,:S0=18d3xdt(E2-1B2),.:S=42d3xdtEB,(8)=e2/hc.S,.[43].,[26,44,45].S[26,44].E,B,,S.=0,S,Z2.,=0,=..6结论和展望,.,,..(),(),.,,.,.,.,[46][47].,.[1]KlitzingKV,DordaG,PepperM.Phys.Rev.Lett.,1980,45:494[2]HalperinBI.Phys.Rev.B,1982,25:2185[3]WenXG.Phys.Rev.B,1990,41:12838[4]WenXG.AdvancesinPhysics,1995,44:405[5]WuTT,YangCN.Phys.Rev.D,1975,12:3845[6]ThoulessDJ,KohmotoM,NightingaleMPetal.Phys.Rev.Lett.,1982,49:405[7]HaldaneFDM.Phys.Rev.Lett.,1988,61:2015[8]HsiangWY,LeeDH.Phys.Rev.A,2001,64:052101[9]AvronJE,SeilerR,SimonB.Phys.Rev.Lett.,1983,51:51[10]DysonFJ.J.ofMath.Phys.,1962,3:140[11]AvronJE,SadunL,SegertJetal.Phys.Rev.Lett.,1988,61:329[12]ZhangSC,HuJP.Science,2001,294:823[13]MurakamiS,NagaosaN,ZhangSC.Science,2003,301:1348[14]KaneCL,MeleEJ.Phys.Rev.Lett.,2005,5:226801[15]YaoY,YeF,QiXLetal.Phys.Rev.B,2007,75:041401[16]XuC,MooreJE.Phys.Rev.B,2006,73:045322[17]KaneCL,MeleEJ.Phys.Rev.Lett.,2005,95:146802[18]WuC,BernevigBA,ZhangSC.Phys.Rev.Lett.,2006,96:106401[19]BernevigBA,HughesTL,ZhangSC.Science,2006,314:1757[20]LiuC,HughesTL,QiXLetal.Phys.Rev.Lett.,2008,100:236601[21]LiJ,ChuRL,JainJKetal.Phys.Rev.Lett.,2009,102:136806[22]JiangH,WangL,SunQFetal.2009.arXiv:0905.4550v1[23]RoyR.2006.arXiv:cond-mat/0607531[24]FuL,KaneCL,MeleEJ.Phys.Rev.Lett.,2007,98:106803[25]MooreJE,BalentsL.Phys.Rev.B,2007,75:121306[26]QiXL,HughesTL,ZhangSC.Phys.Rev.B,2008,78:195424[27]FuL,KaneCL.Phys.Rev.B,2007,76:045302[28]HsiehD,QianD,WrayLetal.Nature,2008,452:970[29]ZhangH,LiuCX,QiXLetal.Nat.Phys.,2009,5:438[30]XiaY,QianD,HsiehDetal.Nat.Phys.,2009,5:398[31]ZhangT,ChengP,ChenXetal.Phys.Rev.Lett.,2009,103:266803[32]ZhangY,HeK,ChangCZetal.2009.arXiv:0911.3706v2[33]ChenJ,QinHJ,YangFetal.2010.arXiv:1003.1534v2[34]YanB,LiuCX,ZhangHJetal.2010.arXiv:1003.0074v1[35]NomuraK,KoshinoM,RyuS.Phys.Rev.Lett.,2007,99:146806[36]LiuQ,LiuCX,XuCetal.Phys.Rev.Lett.,2009,102:156603[37]GaoJ,ChenW,XieXCetal.Phys.Rev.B,2009,80:241302[38]YeF,DingGH,ZhaiHetal.2009.arXiv:1002.0111,tobepublished[39]CastroNetoAH,GuineaF,PeresNMRetal.Rev.Mod.Phys.,2009,81:109[40]NielsenHB,NinomiyaM.Phys.Lett.,1981,B105:21