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光/声拓扑材——从声类石墨烯到拓扑绝缘 E-mail: 大学固体微结构物理国材料科学与工程系-现代工程与应绵NanjingNanjingNanjing

CarriersofInformationand -Charge,Spin,Mass,

EM

--Wavelength:nm,um,--Wavelength:nm,um,•••••Manipulation:MacroscopePropertiesofelectric,magnetic,thermal,Nanjing1969NanjingMicrostructures1969NanjingLargeScaleLargeScale 1947Band-Band-MicrostructuresandPhysicsofRefractindexRefractindexmodulated→Photonic19873RGBwhiteSolid-Nonlinearopticcoeff.→SHG,1980 Nanjing1980MicrostructuresandPhysicsofSurfaceSPPbandwith1998Magneticnegativepermeability,Left-2001

NanjingMicrostructuredMicrostructuredMaterials:Materials+

Nonlinearoptic

Acoustic Photonic

MicrostructuredMaterials

Quantum- Elastic

NegativeεandNanjing

Nonlinearoptic

Acoustic Photonic

MicrostructuredMaterials

Quantum- Elastic

NegativeεandNanjingMicrostructuredartificialstrucutures+materialsPropertiesdependsonmetalanditsforms:R,Cand1、BandTopologicalTimeandArtificialNature2ArtificialNatureShapeandActive

NanjingSurfacephononic NatureMater.16,(2016)Nanjing石墨烯(电子能

人工类“石墨烯”材Nature,490,192

线性色EEvkFvFk2kxy(Dirac点、Dirac费米子类比:人工带隙材料:其它粒子/准粒子:人工“石墨烯”材二维电子(电子能带

(光子能带

PRL.104,043903PRL.104,043903 PRL.113,196803Nat.Mat.13,57 Phys.Rev.B.PRL.113,196803RRm每一个“柱体”可以被视作一个具有质量的弹簧“振子”,本征振动频率: kRRmR 2

t R D

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30MHz-

2000m/s-10000LiNbO3

LiNbO3基‘凸起’微Nanjing

以电铸镍(Ni)为例,其 Ni2+2e-1 法拉第第一、二定律,Ni析出速率rirzFzF 电流效率

r

D0DStep1:析出速度电流效Step2:确定电铸面积(样品总面积*占空比Step3:电铸电流电铸时NanjingSPnC氯化镍:7.5g/L氯化镍:7.5g/LpH值:4.5左Nanjing采用精密电 b “mushroom”

“ring”jingUniversijingUniversi基于LiNbO3基底单片集成实验体Nanjing SAW SAW 1 SAW 0Nanjingelasticenergy I对称Γ0K1称Paul Erwin

Zitterbewegung相对论性量子粒子(例如Schrödinger根据Dirac方程直接推导所.然而 在实际自由相对论性粒子中观到 的振荡频率(1021Hz量级——超短波长接近康普顿波长PRL105,143902PRL105,143902inPhotonicPRL100,153002withUltracoldAtomsPRL101,264303Observingfor2D利用SAW平台观察到

L=16L=20(Dirac频

(Dirac锥以外

L=16L=20提供了一个新的量子模拟实验平台(Quantum优势:1.单片集成/低成本 信噪比 ;3.易于设计及调 NatureMater.16,(2016)高频微波声子的:集成微波声学器新型无线传感器慢波的概念引入声表面波有助于实现具有最佳“延时-带宽积”的慢声器 实验测量声表声速最低慢至1/25,达140米/ NanjingTopologyinTopology,asawell-definedmathematicaldiscipline,originatesintheearlypartoftwentiethcentury,butsomeisolatedresultscanbetracedbackseveralThesevenbridgesofKönigsbergEuler'spolyhedron

FourcolormapNanjingTopologyinreal

2016NobelPrizeinDavidJ.J.Michael"fortheoreticaldiscoveriesoftopologicaltransitionsandtopologicalphasesofmomentumGauss 2(1g)sKdA/(2

CBcds/(2Cg Brand-newglobal

NanjingTwocasesofgeometryInclassicalandquantumthegeometricphase,orcommonlyBerryaphasedifferenceacquiredoverthecourseofacycle,whenasystemissubjectedtocyclicadiabaticfiberItresultsfromthegeometricalpropertiesoftheparameterfiberBerryBerry

vectortangenttothe “cyclicadiabatic

NanjingComparedtowell-knownABInthecaseoftheAharonov–Bohmeffect,theadiabaticparameteristhemagneticfieldenclosedbytwointerferencepathstoformaloop.PhaseexperiencingzeroB,butnon-zeroL.Luetc.Naturephotonics8,821

NanjingHall ChernNumber 整数量子霍尔效应 分数量子霍尔效应拓扑绝缘体:量子自旋霍尔效应拓扑绝缘体:量子自旋霍尔效应Nanjing Symmetry-protectedtopological(SPT)NanjingGaplessedgeInsulatinginbulkbutmetallicontheUnidirectionalpseudo-spindependentOne-wayandbackscatteringRobustnessaslongassymmetryisi.e.QSHandtopologicalinsulatorprotected 问 :1、声子是玻色子,而电子是费米2、电子满足Kramers简并,声子不 整数量子霍尔效应 分数量子霍尔效应量子反常霍尔效应 拓扑绝缘体:量子自旋霍尔效应NanjingElectronsVsNanjingElectronTopologicalStatesvsOpticalandAcousticQuantumHallQuantumSpin

Thouless,D.J.et.al.Phys.Rev.Lett.49,405(1982);Klitzing,K.V.,Dorda,G.&Pepper,M.Phys.Rev.Lett.45,494(1980);Bernevig,B.A.,Hughes,T.L.&Zhang,S.-C.Science314,1757(2006);Hasan,Z.&Kane,C.L.Rev.Mod.Phys.82,3045(2010).Lindner,N.H.et.al.NaturePhys.7,NanjingPhotonicspinPhotonicIntegerQuantumHallF.D.M.Haldaneetal.PRL.100,013904Z.Wangetal.PRL.100,Z.Wangetal.Nature461,Photonictopologicaledgestates:

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Z.Yangetal.PRL,114114301A.B.Khanikaevetal.Nat.Commun.6,8260NanjingPhononicTopologicalIncreasedegreesofAccidentaldegeneracyofdoubleDiracconesinaphononicZ.-G.Chenetal.ScientificReports4,4613NanjingNanjingNanjing1111C.He,etalNat.Phys.14,NanjingC.He,etalNat.Phys.14,NanjingC.Heetal.arXiv:1512.03273k.pmethodtocalculatetopological4×4

basis

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BM<0---anordinaryphase;BM>0---atopologicalCs=-1,+1,-1,+1fromlowertoupperfourbandsH.Li,etal,PRL110,NanjingProjectedenergyNanjingBulkbandgapandNanjingAcousticone-wayspin-dependentSpin SpinNanjingRobustone-waysoundNanjing ChengHe,etalNat.Phys.14,1124更鲁棒的实验体系,避免了传统凝聚态拓扑绝缘体更鲁棒的实验体系,避免了传统凝聚态拓扑绝缘体

被科 》一文作为年度5大热Nanjing+_PhotonicTopological+_B.Khanikaev,G.ShvetsetNat.Mater.12,233(2013),UTNanjing ogueofQSH LeftCircularPolarization(LCP)&RightCircular

Photonic-TI

Khanikaev,etal.Nat.Mater. Kong,J.A.Theoryofelectromagneticwaves.(Wiley,1975) Sihvola,A.H.&Lindell,I.V.IeiceTElectron78,1383-1390(1995).Nanjing ogueofQSHviaLCP& K:ComplexEigenKramersNanjingMotivation:spoilrobustnesswithoutbreaking

fT2f

bT2bNanjingNanjing What’stherealprotectedA.Khanikaev,etal.Nat.Mater.12,233PhotonictopologicalinsulatorviaLCP&Nat.Mater.12,233Nat.Commun.5,5782

PRL,114127401arXiv:1601.01311KramersdegeneracyNanjingPointgroup:622/6mm(or422Zhao,J.etal..PRB77,075126(2008);PLA372,486Elastic5700Kgm-C33=162C44=43e14=1.512Cm-5000Kgm-C33=269.5C44=45.3m15=550NA-m-5350Kgm-C33=215.75C44=44.15Huang,J.H.&Kuo,W.-S.J.Appl.Phys.81,1378-1386(1997).;Pan,E.Z.angew.Math.Phys.53,815-838 NanjingD(z)(

G2f(z)fY n jk (

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upperUnbrokenUnbrokenUnbrokenUnbrokenUnbrokenBrokenTight-bindingapproximation(TBA)&BulkEdge Fu,L.&Kane,C.L.Phys.Rev.B76,045302 Nanjing ogueofQSHviaTE& C.He,M.H.Lu,Y.F.Chenetal.arXiv:1401.5603v1NanjingMotivation:spoilrobustnesswithoutbreakingC.He,M.H.RobustnessbrokenC.He,M.H.UnbrokenTb,BrokenNanjingProtected C.He,X.C.Sun,M.H.Lu,Y.F.Chenetal.PNAS113,X.C.Sun,etal,Prog.QuantumElectronics55,52Nanjing QuantumspinHalleffect(2D usingspin-orbitcouplinginsteadofstaggeredmagneticHaldaneHh H(k)

HhC.L.KaneandE.J.Mele,Phys.Rev.Lett.95,HgTequantum

BandBandinversionBernevig,Hughes,Zhang,Science.314, experiment:Science.318, NanjingWhichsymmetrytoprotecttopologicalinvarianceElectronic

fermionor iyTf

2、twofolddegenerateBlochstatestoKramersfor

cTf2c2Tf

c2HasanHasanMZ,KaneCL,Rev.Mod.Phys.82,(2010)QiX-L,ZhangS-C,Rev.Mod.Phys.83,Nanjing3、spin-orbitinteractionandbandH(k)H H*(k) H(k)T1H(k 1.Fermionwithspin2.Time-reversalṪ21.Fermionwithspin2.Time-reversalṪ2=-1for3.KramersdoubletDegeneracyfor2n+1statesBosonTsymmetrybroken!2nstates!Theedgestatesareonlyprotectedinthepresenceofthetime-symmetry.Lostthetime-reversalsymmetryresultsinatrivialThenumberofedgestatesisonlywell-definedmodSoonlytwotypesofinsulators:noedgestates;1pairofedgeThat’swhytheinsulatorscalledZ2topologicalThisisverydifferentfromIQHE,whichcanhaveanynumberofedgeNanjingBosonicTopologicalInsulators:PhotonandElectron:halfspinTfT2Electron:halfspinTfT2fPhotonandphonon:integralspinT2bNanjingT2pTpHTpz-zBosonicTI:T2pTpHTpz-zNanjing Tb Tb ixz iy

Hz

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Nat.Mater.12,233Nat.Commun.5,5782Phys.Rev.Lett.114,127401Nat.Mater.15,542arXiv:1401.56032、QuadraticorlineardegenerateBloch

1

THT110 i10

NanjingPseudotime-reversalsymmetrytoprotectPhotonProtected C.He,X.C.Sun,M.H.Lu,Y.F.Chenetal.PNASX.C.Sun,etal,Prog.QuantumElectronics55,52-73NanjingPhononicTIs:Blochstates-based 1、FourfolddegenerateBlochstatesandbandphotonicTE longitudinalPhys.Rev.Lett.114,223901 Tp[(/3)Tp[(/3)(2/ 3Kiy3、BHZmodelviak-p2px px

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NanjingNanjing:Nanjing:TopologicalInsulatorsofLambTypesofsonicFluid,Surface,Formsofsonicwaves:Bulk,Surface,ConfinedTypesofconfined——Rayleigh——LambConfinedinImaging TopologicalInsulatorsofelasticwaves:TopologicalInsulatorsofLambTopologicalElasticEdgestate:elasticpseudospin(edgeunderpseudotime-reversalpTp

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21IMAGINGofElasticEdgeNanjingObservationofElasticSpin-MomentumUpwardElasticEnergy

DownwardElasticEnergyOrdinaryInsulator(OI)Pse

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