拓扑绝缘体与拓扑半金属

1拓扑绝缘体与拓扑半金属方忠中科院物理研究所中国工程物理研究院材料科学技术发展会议2目录一、简介二、拓扑绝缘体材料：Bi2Se3，Bi2Te3三、拓扑半金属：HgCr2Se41.简介：拓扑有序态有序态是凝聚态物理研究的基本内涵之一例如：磁有序态、电荷有序态、超导态等局域有序态：对称性破缺导致有序态（朗道对称性破缺理论）1.物态可以用局域序参量描写如：铁磁态的磁化强度M(r)2.相变伴随着对称性破缺如：M(r)的出现破坏了旋转对称性宏观有序态：拓扑有序态（量子物理与几何的完美结合）1.具有拓扑性质的“量子态”2.不能用局域序参量描写，而要用全局拓扑不变量描写3.相变过程并不伴随对称性破缺拓扑“0”拓扑“1”反铁磁铁磁自旋波1.简介：拓扑绝缘体简介拓扑绝缘体：一种全新的拓扑有序态：受时间反演性保护要考虑相对论+量子力学一般绝缘体拓扑绝缘体金属费米能级能带结构表面态体态体态体态理论模型：1.C.L.Kane，PRL(2005)2.S.C.Zhang，PRL(2006)材料实现：1.二维材料：L.Molenkamp,Science(2007)2.三维材料：方忠等，NaturePhys.(2009)(Bi2Te3,Bi2Se3,Sb2Te3)与一般表面态区别：无论如何切样品，表面态总是存在1.简介:Whyedgestates？“Bandtwist”TIVaccumNormalinsulatorBoundaryCuttingBandRingDefinedbytheZ2number(orparityforinversionsystem)Ref:[1]Kane&Mele,PRL(2005).[2]Fu,Kane,Mele,PRL(2007)[3]Fu,Kane,PRB(2007).TopologicalInsulators:1.Insulatingbulk2.Conductingsurface3.DefinedbytheZ2quantumnumber4.SurfacestateisprotectedbyTreversalsymmetry5.Robustagainstnone-MdisordersSurfaceStateordinaryInsulatorSurfaceStateTopologicalInsulator++++----“能带twist”1.简介:DifferentSurfacestates1.简介：SurfacestatevsGrapheneGrapheneSurfacestateofTIK'KΓ（1）1/4ofGraphene，spinsplitting，T-invariant（2）2DEGwithoutmass（3）KlienParadox（4）linearn~E，linearσ~E，linearm~E（5）QHE？Localization？（6）Multi-ferroic？（1）psudo-spin（2）KlienParadox（3）linearn~E，linearσ~E，linearm~E（4）Localization？（5）Universalσ？（6）......1.简介：拓扑有序态新奇量子现象除非破坏性剪断拓扑有序量子态的优点：1.“0”与“1”严格区分，无微扰过程，不怕干扰、噪声2.与“奇点”密切相关，在边界上会有特殊量子态≠信息高速公路：极低电阻、极低能耗各行其道，永不混杂遇到杂质，自动绕行鱼目混杂，杂乱无章遇到杂质，会被散射普通态拓扑有序态奇点面包圈球过渡1.简介：量子霍尔效应（IQHE）最早认识的拓扑有序态是----量子霍尔效应量子Hall效应中间绝缘边界导电朗道能级体态边缘态边缘态1.VeryStable2.Nobackscattering(Edgestatecannotlocalize)问题：1.需要强磁场、极低温2.破坏了时间反演对称性3.只存在于二维系统4.不是拓扑绝缘体（需要借助于外磁场）1.简介：拓扑绝缘体简介（1）基础科学发展：全新的物理概念、现象、效应1.新奇量子效应2.基本物理常数的确定（2）下一代电子技术：革新性的进步1.准零能耗电子器件：无电阻的“理想导线”2.“电”与“磁”交叉调控，巨大响应3.能源器件：热电效应、非线性光学4.拓扑催化5.核燃料问题：高熔点、高热导（3）国际发展的趋势：是当前国际发展的前沿1.欧美已投入巨资2.日本正在启动重要性：1.简介:FamilyofTIs?2D3DT-brokenT-invariantT-invariantT-BrokenKondoQHEQSHETopologicalBandInsulatorQAHEAndersonMott......EdgeStatesTKNNZ2ChernnumberSurfaceStatesSemi-metalFemipoints(inbulk)2.拓扑绝缘体：T-brokenvsT-InvariantQSHEinHgTe/CdTe(S.C.Zhang,SCIENCE2006)QHE2.拓扑绝缘体：Materials.Guidelines:1.Semiconductorwithinvertedbandstructure2.StrongSOC+-++--GapopeningduetoSOC“twistedband”困难：Realmaterialsfor3DTI?+++---PredictionsforBi2Te3family:BasicProperties1.Found70yearsago.Naturwissenschaften,27,133(1939)2.Semi-conductor.OpticalGap~0.2eVJ.Phys.Chem.Solids,2,240(1957)3.Oneofthebestthermoelecticmaterials.ZT~1atroomT4.Easytobesynthesized5.WholeFamily:Bi2Te3,Sb2Te3Bi2Se3,Sb2Se32.拓扑绝缘体：Bi2Te3,Bi2Se3,Sb2Te3CrystalStructureICenter2.拓扑绝缘体：Bi2Te3,Bi2Se3,Sb2Te3BandStructureBi2Se31.OnlyGammaPointisrelavant.2.SOCwillinvertthebandsatGamma.3.Gapisaround0.3eV.WithoutSOCWithSOC+-++--ab-initioSurfaceStates:Bi2Se3hasthebiggestGaparound0.3eVH.J.Zhang,et.al.,NaturePhys.(2009)PenetrationDepthofSurfacestate,2nm2.Materials：Bi2Te3,Bi2Se3,Sb2Te3W.Zhang,et.al.,NewJ.Phys,12,065013(2010)ChiralSpintextureY.L.Chen,et.al.SCIENCE(2009)Bi2Te3Y.Xia,et.al.NaturePhysics(2009)Bi2Se32.TIMaterials：Exp.evidenceARPES-50meV0V50meV100meV150meV200meV250meV300meV0.100.150.200.25-0.2-0.10.00.10.20.30.4Energy(eV)q(A-1)UpperTerraceT.Zhang,et.al.,PRL(2009).2.TIMaterials：Exp.evidenceAbsenceofback-scattering2.TImaterials：拓扑绝缘体在压力下的超导态：靳常青，PNAS（2011）孙立玲，等，PRB(2011).Editor'sSuggestion拓扑超导态？2.拓扑绝缘体：最新进展磁性拓扑绝缘体----量子化反常Hall效应量子Hall效应QuantumHallstateBEnergykConductionbandValencebandQuantumAnomalousHallstateMEnergykConductionbandValencebandQuantumSpinHallstatekConductionbandValencebandEnergyedgeBi2Se3filmdopedwithCrorFe量子反常Hall效应方忠、戴希等，SCIENCE(2010)无需外加磁场实现量子Hall效应！已获得初步实验证实：何柯，马旭村,薛其坤等，Cr-Bi2Te3-Sb2Te3film，arxiv：1108.4754(2011).CrystalStructure:T417K,α-Ag2Te,anti-fluorite(Fm3m)T417K,β-Ag2Te,distorted(P21/c)2.TIMaterials：Ag2TeCubic:a,b,cGaAs2.TIMaterials：Ag2TeInvertedBandStructureofα-Ag2TeSimilartoHgTeГ6Г7Г8S-bandP-bandsGaASГ6Г7Г8HgTe2.TIMaterials：Ag2Teβ-Ag2Te,gap=80meVW.Zhang,et.al.,PRL106,156808(2011).QuantumMagneto-resistanceinAg2+δTe?Super-linearMRR.Xu,et.al.,Nature(1997).ConventionalMR:Abrikosov'sQuantumMR:LinearDispersionisImportant!LandauLevelSpacing.B3.拓扑半金属：MomentumSpaceTopologyThreedistinctstableclassesin3D:InsulatorsSemi-metalFermisurfaceEfMetalsNofermisurfaceFemipoints(inbulk)Fermiarcs(onsurface)NormalInsulators+TopologicalInsulators(WeylpointsatBoundary)OurSubjects3.拓扑半金属:FamilyofTIs?2D3DT-brokenT-invariantT-invariantT-BrokenKondoQHEQSHETopologicalBandInsulatorQAHEAndersonMott......EdgeStatesTKNNZ2ChernnumberSurfaceStatesSemi-metalFemipoints(inbulk)3.Semimetals:From2Dto3DwithoutTRS？2DChernInsulators:+-++--GapopeningduetoSOC+++---3D:(1)Weak3DChernInsulators:(2)Strong3D--Anyanalogy?Chernsemi-metal:TimeReversalPolarizatio