半导体中与自旋相关的新奇量子现象
|
摘要
自旋电子学的研究是当前凝聚态物理领域中最重要的研究课题之一。自旋电子学是利用电子的自旋而非电子的电荷作为信息载体而发展的物理和电子器件研究的分支领域。如何操控和探测电子自旋便成为了自旋电子学的关键问题。本文首先回顾并总结了自旋电子学研究的历史与现状，然后讨论了作为自旋信息传输核心的自旋流，并从自旋流的基本性质出发，简要回顾了目前国际上探测自旋流的实验手段，鉴于目前尚无实时、原位测量纯自旋流的实验手段，我们研究了半导体中纯自旋流的线性光学(法拉第旋转)和二阶非线性光学效应，并提出以此直接测量半导体中纯自旋流的理论。我们预言的自旋流的倍频效应很快得到了实验证实。接着我们讨论了III-V族半导体量子点中电子自旋的退相干问题，提出了通过非线性光学实现自旋回波的理论。
寻找和研究新的物质态一直是凝聚态物理研究的热点。在半导体以及低维结构中，电子的自旋轨道耦合会导致一些新奇的量子态。这些新的量子态也导致自旋电子学新的发展。我们的研究主要集中在拓扑绝缘体，一类表面存在无能隙金属态的绝缘体。二量子自旋Hall效应实际上是二维拓扑绝缘体的物理上的表现。我们讨论了拓扑绝缘体的基本性质以及场论描述，进一步探讨了拓扑绝缘体中的电子电子相互作用。我们从拓扑绝缘体体内的磁性涨落出发，指出当某种反铁磁长程序存在时，体系将会出现新的元激发-动力学轴子，其与光子耦合形成新的极化激元。我们称这种绝缘体为拓扑磁性绝缘体，并且研究了具有Corundum结构的过渡金属氧化物，指出其有可能实现拓扑磁性绝缘体。拓扑绝缘体的新奇之处在于表面存在奇数个受时间反演对称保护的Dirac电子态，因此最后我们讨论了拓扑表面态的有效模型，并且研究了其Landau能级量子化和准粒子相干，部分结果很快被实验证实。
The research on spin-based electronics (spintronics) is one of the most importantsubjects in modern condensed matter physics. In spintronics where it is not the electroncharge but the electron spin that carries the information. The control and probe of electronspin are indispensable parts of spintronics. In this thesis, we first review the history andcurrent status on spintronics research. Then we discuss pure spin currents (PSCs) whichplay a key role in information transfer. Starting from the basic properties of PSCs and thecurrent experimental techniques for PSCs measurements, we present our theory on opticalefects of PSCs in the direct-gap semiconductors, i.e. the Faraday rotation and nonlinearoptics, which provide a direct measurement of PSCs in semiconductors. Soon after theproposal, the second-harmonics generation of PSCs has been experimental verified. Wehave also studied the electron spin decoherence in III-V semiconductor quantum dots, andproposed to explore the electromagnetic vacuum fluctuations for spin-flip control and touse nonlinear optical spectroscopy to realized the spin echo.
Searching new states of matter is the key part in condensed matter physics. The spin-orbit coupling (SOC) in semiconductors and low-dimensional structures will give rise tomany novel quantum states, which brings new development to spintronics. Here we fo-cus on topological insulators (TIs), which are characterized by the fully bulk insulatinggaps and gapless surface states. Quantum spin Hall efect (QSHE) is a physical realiza-tion of two-dimensional TIs. We discuss the basic properties of TIs and its field theorydescription. Then we study the electron-electron interactions in TIs, we find that magneticfluctuations of TIs coupled to the electromagnetic fields behave like the axions. The axionfield hybridizes with photons, leading to an axion polariton. We refer such an antiferro-magnetic insulator as a ‘topological magnetic insulators’(TMI). Then we study a transitionmetal oxide of corundum structure, in which both SOC and electron-electron interactionplay crucial roles, it may realize TMI phase. Many novel quantum phenomena resultedfrom the topological surface states which are protected by time-reversal symmetry, finallywe discuss the Landau quantization and quasi-particle interference of surface states.
寻找和研究新的物质态一直是凝聚态物理研究的热点。在半导体以及低维结构中，电子的自旋轨道耦合会导致一些新奇的量子态。这些新的量子态也导致自旋电子学新的发展。我们的研究主要集中在拓扑绝缘体，一类表面存在无能隙金属态的绝缘体。二量子自旋Hall效应实际上是二维拓扑绝缘体的物理上的表现。我们讨论了拓扑绝缘体的基本性质以及场论描述，进一步探讨了拓扑绝缘体中的电子电子相互作用。我们从拓扑绝缘体体内的磁性涨落出发，指出当某种反铁磁长程序存在时，体系将会出现新的元激发-动力学轴子，其与光子耦合形成新的极化激元。我们称这种绝缘体为拓扑磁性绝缘体，并且研究了具有Corundum结构的过渡金属氧化物，指出其有可能实现拓扑磁性绝缘体。拓扑绝缘体的新奇之处在于表面存在奇数个受时间反演对称保护的Dirac电子态，因此最后我们讨论了拓扑表面态的有效模型，并且研究了其Landau能级量子化和准粒子相干，部分结果很快被实验证实。
The research on spin-based electronics (spintronics) is one of the most importantsubjects in modern condensed matter physics. In spintronics where it is not the electroncharge but the electron spin that carries the information. The control and probe of electronspin are indispensable parts of spintronics. In this thesis, we first review the history andcurrent status on spintronics research. Then we discuss pure spin currents (PSCs) whichplay a key role in information transfer. Starting from the basic properties of PSCs and thecurrent experimental techniques for PSCs measurements, we present our theory on opticalefects of PSCs in the direct-gap semiconductors, i.e. the Faraday rotation and nonlinearoptics, which provide a direct measurement of PSCs in semiconductors. Soon after theproposal, the second-harmonics generation of PSCs has been experimental verified. Wehave also studied the electron spin decoherence in III-V semiconductor quantum dots, andproposed to explore the electromagnetic vacuum fluctuations for spin-flip control and touse nonlinear optical spectroscopy to realized the spin echo.
Searching new states of matter is the key part in condensed matter physics. The spin-orbit coupling (SOC) in semiconductors and low-dimensional structures will give rise tomany novel quantum states, which brings new development to spintronics. Here we fo-cus on topological insulators (TIs), which are characterized by the fully bulk insulatinggaps and gapless surface states. Quantum spin Hall efect (QSHE) is a physical realiza-tion of two-dimensional TIs. We discuss the basic properties of TIs and its field theorydescription. Then we study the electron-electron interactions in TIs, we find that magneticfluctuations of TIs coupled to the electromagnetic fields behave like the axions. The axionfield hybridizes with photons, leading to an axion polariton. We refer such an antiferro-magnetic insulator as a ‘topological magnetic insulators’(TMI). Then we study a transitionmetal oxide of corundum structure, in which both SOC and electron-electron interactionplay crucial roles, it may realize TMI phase. Many novel quantum phenomena resultedfrom the topological surface states which are protected by time-reversal symmetry, finallywe discuss the Landau quantization and quasi-particle interference of surface states.
引文
[1] Wolf S A, Awschalom D D, Buhrman R A, et al. Spintronics: A Spin-Based Electronics Visionfor the Future. Science,2001,294(5546):1488–1495.
[2]Z utic′I, Fabian J, Das Sarma S. Spintronics: Fundamentals and applications. Rev. Mod. Phys.,2004,76(2):323–410.
[3] Awschalom D D, Flatte M E. Challenges for semiconductor spintronics. Nat. Phys.,2007,3:153.
[4] Awschalom D D, Loss D, Samarth N. Semiconductor Spintronics and Quantum Computation.Berlin: Springer,2002.
[5] Baibich M N, Broto J M, Fert A, et al. Giant Magnetoresistance of (001)Fe/(001)Cr MagneticSuperlattices. Phys. Rev. Lett.,1988,61(21):2472–2475.
[6] Datta S, Das B. Electronic analog of the electro-optic modulator. Appl. Phys. Lett.,1990,56:665.
[7] Meier F, Zakharchenya B P. Optical Orientation. Amsterdam: North-Holland,1984:12–71.
[8] Bhat R D R, Sipe J E. Optically Injected Spin Currents in Semiconductors. Phys. Rev. Lett.,2000,85(25):5432–5435.
[9] Schmidt G, Ferrand D, Molenkamp L W, et al. Fundamental obstacle for electrical spin injectionfrom a ferromagnetic metal into a difusive semiconductor. Phys. Rev. B,2000,62(8):R4790–R4793.
[10] Rashba E I. Theory of electrical spin injection: Tunnel contacts as a solution of the conductivitymismatch problem. Phys. Rev. B,2000,62(24):R16267–R16270.
[11] Zhu H J, Ramsteiner M, Kostial H, et al. Room-Temperature Spin Injection from Fe into GaAs.Phys. Rev. Lett.,2001,87(1):016601.
[12] Hirsch J E. Spin Hall Efect. Phys. Rev. Lett.,1999,83(9):1834–1837.
[13] Murakami S, Nagaosa N, Zhang S C. Dissipationless Quantum Spin Current at Room Temper-ature. Science,2003,301(5638):1348–1351.
[14] Sinova J, Culcer D, Niu Q, et al. Universal Intrinsic Spin Hall Efect. Phys. Rev. Lett.,2004,92(12):126603.
[15] Dyakonov M I, Perel V I. Current-induced spin orientation of electrons in semiconductors.Phys. Lett. A,1971,35:459.
[16] Kato Y, Myers R C, Gossard A C, et al. Coherent spin manipulation without magnetic fields instrained semiconductors. Nature,2004,427:50.
[17] Silov A Y, Blajnov P A, Wolter J H, et al. Current-induced spin polarization at a single hetero-junction. Appl. Phys. Lett.,2004,85:5929.
[18] Hall E. On a New Action of the Magnet on Electric Currents. Am. J. Math.,1879,2:287.
[19] Inoue J, Ohno H. Taking the Hall Efect for a Spin. Science,2005,309(5743):2004–2005.
[20] Wunderlich J, Park B G, Irvine A C, et al. Spin Hall Efect Transistor. Science,2010,330(6012):1801–1804.
[21] Qi X L, Zhang S C. The quantum spin Hall efect and topological insulators. Phys. Tod.,2010,63(1):33–38.
[22] Moore J E. The birth of topological insulators. Nature,2010,464:194–198.
[23] Hasan M Z, Kane C L. Colloquium: Topological insulators. Rev. Mod. Phys.,2010,82(4):3045–3067.
[24] Wang J, Zhu B F, Liu R B. Proposal for Direct Measurement of a Pure Spin Current by aPolarized Light Beam. Phys. Rev. Lett.,2008,100(8):086603.
[25] Wang J, Zhu B F, Liu R B. Second-Order Nonlinear Optical Efects of Spin Currents. Phys.Rev. Lett.,2010,104(25):256601.
[26] Weraka L K, Zhao H. Observation of second-harmonic generation induced by pure spin currents.Nat. Phys.,2010,6:875.
[27] Cirac J I, Zoller P. A scalable quantum computer with ions in an array of microtraps. Nature,2000,404:579.
[28] Kielpinski D, Monroe C, Wineland D J. Architecture for a large-scale ion-trap quantum com-puter. Nature,2002,417:709.
[29] Yamamoto T, Pashkin Y A, Astafiev O, et al. Demonstration of conditional gate operation usingsuperconducting charge qubits. Nature,2003,425:941.
[30] O’Brien J L, Pryde G J, White A G, et al. Demonstration of an all-optical quantum controlled-NOT gate. Nature,2003,426:264.
[31] Vandersypen L M K, Stefen M, Breyta G, et al. Experimental realization of Shor’s quantumfactoring algorithm using nuclear magnetic resonance. Nature,2001,414:883.
[32] Liu R B, Yao W, Sham L J. Quantum computation by optical control of electron spins. Adv.Phys.,2010,59:703.
[33] Petta J R, Johnson A C, Taylor J M, et al. Coherent Manipulation of Coupled Electron Spins inSemiconductor Quantum Dots. Science,2005,309(5744):2180–2184.
[34] Greilich A, Yakovlev D R, Shabaev A, et al. Mode Locking of Electron Spin Coherences inSingly Charged Quantum Dots. Science,2006,313(5785):341–345.
[35] Bracker A S, Stinaf E A, Gammon D, et al. Optical Pumping of the Electronic and NuclearSpin of Single Charge-Tunable Quantum Dots. Phys. Rev. Lett.,2005,94(4):047402.
[36] Reilly D J, Taylor J M, Petta J R, et al. Suppressing Spin Qubit Dephasing by Nuclear StatePreparation. Science,2008,321(5890):817–821.
[37] Jelezko F, Gaebel T, Popa I, et al. Observation of Coherent Oscillation of a Single NuclearSpin and Realization of a Two-Qubit Conditional Quantum Gate. Phys. Rev. Lett.,2004,93(13):130501.
[38] Taylor J M, Marcus C M, Lukin M D. Long-Lived Memory for Mesoscopic Quantum Bits.Phys. Rev. Lett.,2003,90(20):206803.
[39] Uhrig G S. Keeping a Quantum Bit Alive by Optimized π-Pulse Sequences. Phys. Rev. Lett.,2007,98(10):100504.
[40] Yang W, Liu R B. Universality of Uhrig Dynamical Decoupling for Suppressing Qubit PureDephasing and Relaxation. Phys. Rev. Lett.,2008,101(18):180403.
[41] Greilich A, Shabaev A, Yakovlev D R, et al. Nuclei-Induced Frequency Focusing of ElectronSpin Coherence. Science,2007,317(5846):1896–1899.
[42] Xu X, Yao W, Sun B, et al. Optically controlled locking of the nuclear field via coherent dark-state spectroscopy. Nature,2009,459:1105.
[43] Sham L J, Rice T M. Many-Particle Derivation of the Efective-Mass Equation for the WannierExciton. Phys. Rev.,1966,144(2):708–714.
[44] Li X, Wu Y, Steel D, et al. An All-Optical Quantum Gate in a Semiconductor Quantum Dot.Science,2003,301(5634):809–811.
[45] Wang J, Liu R B, Zhu B F, et al. Coherent spin control by electromagnetic vacuum fluctuations.Phys. Rev. A,2011,83(5):053833.
[46] Anderson P W. Basic Notions of Condensed Matter Physics. Westview Press,1997:57–87.
[47] Landau L D, Lifshitz E M. Statistical Physics. Oxford: Pergamon Press,1980:1–10.
[48] Thouless D J, Kohmoto M, Nightingale M P, et al. Quantized Hall Conductance in a Two-Dimensional Periodic Potential. Phys. Rev. Lett.,1982,49(6):405–408.
[49] Wen X G. Topological orders and Edge excitations in FQH states. Adv. Phys.,1995,44:405.
[50] Kane C L, Mele E J. Quantum Spin Hall Efect in Graphene. Phys. Rev. Lett.,2005,95(22):226801.
[51] Kane C L, Mele E J. Z2Topological Order and the Quantum Spin Hall Efect. Phys. Rev. Lett.,2005,95(14):146802.
[52] Bernevig B A, Zhang S C. Quantum Spin Hall Efect. Phys. Rev. Lett.,2006,96(10):106802.
[53] Bernevig B A, Hughes T L, Zhang S C. Quantum Spin Hall Efect and Topological PhaseTransition in HgTe Quantum Wells. Science,2006,314(5806):1757–1761.
[54] Fu L, Kane C L, Mele E J. Topological Insulators in Three Dimensions. Phys. Rev. Lett.,2007,98(10):106803.
[55] Fu L, Kane C L. Topological insulators with inversion symmetry. Phys. Rev. B,2007,76(4):045302.
[56] Moore J E, Balents L. Topological invariants of time-reversal-invariant band structures. Phys.Rev. B,2007,75(12):121306.
[57] Roy R. Z2classification of quantum spin Hall systems: An approach using time-reversal invari-ance. Phys. Rev. B,2009,79(19):195321.
[58] Ko¨nig M, Wiedmann S, Bru¨ne C, et al. Quantum Spin Hall Insulator State in HgTe QuantumWells. Science,2007,318(5851):766–770.
[59] Hsieh D, Qian D, Wray L, et al. A topological Dirac insulator in a quantum spin Hall phase.Nature,2008,452:970–974.
[60] Xia Y, Qian D, Hsieh D, et al. Observation of a large-gap topological-insulator class with asingle Dirac cone on the surface. Nat. Phys.,2009,5:398–402.
[61] Zhang H, Liu C X, Qi X L, et al. Topological insulators in Bi2Se3, Bi2Te3and Sb2Te3with asingle Dirac cone on the surface. Nat. Phys.,2009,5(6):438–442.
[62] Klitzing K v, Dorda G, Pepper M. New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance. Phys. Rev. Lett.,1980,45(6):494–497.
[63] Laughlin R B. Quantized Hall conductivity in two dimensions. Phys. Rev. B,1981,23(10):5632–5633.
[64] Bu¨ttiker M. Four-Terminal Phase-Coherent Conductance. Phys. Rev. Lett.,1986,57(14):1761–1764.
[65] Hatsugai Y. Chern number and edge states in the integer quantum Hall efect. Phys. Rev. Lett.,1993,71(22):3697–3700.
[66] Datta S. Electronic Transport in Mesoscopic Systems. New York: Cambridge University,1989:78–99.
[67] Redlich A N. Gauge Noninvariance and Parity Nonconservation of Three-DimensionalFermions. Phys. Rev. Lett.,1984,52(1):18–21.
[68] Semenof G W. Condensed-Matter Simulation of a Three-Dimensional Anomaly. Phys. Rev.Lett.,1984,53(26):2449–2452.
[69] Wu C, Bernevig B A, Zhang S C. Helical Liquid and the Edge of Quantum Spin Hall Systems.Phys. Rev. Lett.,2006,96(10):106401.
[70] Xu C, Moore J E. Stability of the quantum spin Hall efect: Efects of interactions, disorder, andZ2topology. Phys. Rev. B,2006,73(4):045322.
[71] Huertas-Hernando D, Guinea F, Brataas A. Spin-orbit coupling in curved graphene, fullerenes,nanotubes, and nanotube caps. Phys. Rev. B,2006,74(15):155426.
[72] Min H, Hill J E, Sinitsyn N A, et al. Intrinsic and Rashba spin-orbit interactions in graphenesheets. Phys. Rev. B,2006,74(16):165310.
[73] Yao Y, Ye F, Qi X L, et al. Spin-orbit gap of graphene: First-principles calculations. Phys. Rev.B,2007,75(4):041401.
[74] Roth A, Brüne C, Buhmann H, et al. Nonlocal Transport in the Quantum Spin Hall State.Science,2009,325(5938):294–297.
[75] Hsieh D, Xia Y, Wray L, et al. Observation of Unconventional Quantum Spin Textures inTopological Insulators. Science,2009,323(5916):919–922.
[76] Hsieh D, Xia Y, Qian D, et al. A tunable topological insulator in the spin helical Dirac transportregime. Nature,2009,460:1101–1106.
[77] Chen Y L, Analytis J G, Chu J H, et al. Experimental Realization of a Three-DimensionalTopological Insulator Bi2Te3. Science,2009,325(5937):178–181.
[78] Fu L. Hexagonal Warping Efects in the Surface States of the Topological Insulator Bi2Te3.Phys. Rev. Lett.,2009,103(26):266801.
[79] M Zahid Hasan H L, Bansil A. Warping the cone on a Topological Insulator. Physics,2009,2:108.
[80] Zhang T, Cheng P, Chen X, et al. Experimental Demonstration of Topological Surface StatesProtected by Time-Reversal Symmetry. Phys. Rev. Lett.,2009,103(26):266803.
[81] Alpichshev Z, Analytis J G, Chu J H, et al. STM Imaging of Electronic Waves on the Surfaceof Bi2Te3: Topologically Protected Surface States and Hexagonal Warping Efects. Phys. Rev.Lett.,2010,104(1):016401.
[82] Hsieh D, Xia Y, Qian D, et al. Observation of Time-Reversal-Protected Single-Dirac-ConeTopological-Insulator States in Bi2Te3and Sb2Te3. Phys. Rev. Lett.,2009,103(14):146401.
[83] Wang G, Zhu X, Wen J, et al. Atomically smooth ultrathin films of topological insulator Sb2Te3.Nano Research,2010,3:874–880.
[84] Chadov S, Qi X L, Ku¨bler J, et al. Tunable multifunctional topological insulators in ternaryHeusler compounds. Nat. Mat.,2010,9:541.
[85] Lin H, Wray L A, Xia Y, et al. Half-Heusler ternary compounds as new multifunctional experi-mental platforms for topological quantum phenomena. Nat. Mat.,2010,9:546.
[86] Sato T, Segawa K, Guo H, et al. Direct Evidence for the Dirac-Cone Topological Surface Statesin the Ternary Chalcogenide TlBiSe2. Phys. Rev. Lett.,2010,105(13):136802.
[87] Chen Y L, Liu Z K, Analytis J G, et al. Single Dirac Cone Topological Surface State and UnusualThermoelectric Property of Compounds from a New Topological Insulator Family. Phys. Rev.Lett.,2010,105(26):266401.
[88] Nielsen H B, Ninomiya N. Absence of nretrinos on a lattice (I). Proof by homotopy theory. Nul.Phys. B,1981,185:20.
[89] Nielsen H B, Ninomiya N. Absence of nretrinos on a lattice (II). Intuitive topological proof.Nul. Phys. B,1981,193:173.
[90] Bousso R. The holographic principle. Rev. Mod. Phys.,2002,74(3):825–874.
[91] Sharma P. How to Create a Spin Current. Science,2005,307(5709):531–533.
[92] Shi J, Zhang P, Xiao D, et al. Proper Definition of Spin Current in Spin-Orbit Coupled Systems.Phys. Rev. Lett.,2006,96(7):076604.
[93] Kikkawa J M, Awschalom D D. Lateral drag of spin coherence in gallium arsenide. Nature,1999,397:139.
[94] Stephens J, Berezovsky J, McGuire J P, et al. Spin Accumulation in Forward-BiasedMnAs/GaAs Schottky Diodes. Phys. Rev. Lett.,2004,93(9):097602.
[95] Crooker S A, Furis M, Lou X, et al. Imaging Spin Transport in Lateral Ferromag-net/Semiconductor Structures. Science,2005,309(5744):2191–2195.
[96] Zhang S. Spin Hall Efect in the Presence of Spin Difusion. Phys. Rev. Lett.,2000,85(2):393–396.
[97] Kato Y K, Myers R C, Gossard A C, et al. Observation of the Spin Hall Efect in Semiconduc-tors. Science,2004,306(5703):1910–1913.
[98] Wunderlich J, Kaestner B, Sinova J, et al. Experimental Observation of the Spin-Hall Efectin a Two-Dimensional Spin-Orbit Coupled Semiconductor System. Phys. Rev. Lett.,2005,94(4):047204.
[99] Zhao H, Loren E J, Driel H M, et al. Coherence Control of Hall Charge and Spin Currents. Phys.Rev. Lett.,2006,96(24):246601.
[100] Valenzuela S O, Tinkham M. Direct electronic measurement of the spin Hall efect. Nature,2006,442:176.
[101] Kimura T, Otani Y, Sato T, et al. Room-Temperature Reversible Spin Hall Efect. Phys. Rev.Lett.,2007,98(15):156601.
[102] Seki T, Hasegawa Y, Mitani S, et al. Giant spin Hall efect in perpendicularly spin-polarizedFePt/Au devices. Nat. Mat.,2008,7:125.
[103] Cui X D, Shen S Q, Li J, et al. Observation of electric current induced by optically injected spincurrent. Appl. Phys. Lett.,2007,90(24):242115.
[104] Ganichev S D, Bel’kov1V V, Tarasenko S A, et al. Zero-bias spin separation. Nat. Phys.,2006,2:609.
[105] Ganichev S D, Danilov S N, Bel’kov V V, et al. Pure spin currents induced by spin-dependentscattering processes in SiGe quantum well structures. Phys. Rev. B,2007,75(15):155317.
[106] Coleman S, Wess J, Zumino B. Structure of Phenomenological Lagrangians. I. Phys. Rev.,1969,177(5):2239–2247.
[107] Callan C G, Coleman S, Wess J, et al. Structure of Phenomenological Lagrangians. II. Phys.Rev.,1969,177(5):2247–2250.
[108] Jones R C. A New Calculus for the Treatment of Optical Systems. J. Opt. Soc. Am.,1941,31:488.
[109] Zvezdin A K, Kotov V A. Modern Magnetooptics and Magnetooptical Materials. New York:Taylor and Francis Group,1997:1–25.
[110] Yu P Y, Cardona M. Fundamentals of Semiconductors: Physics and Material Properties.3rd eded., Berlin: Springer-Verlag,2005:63–77.
[111] Paul W, Moss T S. Handbook on Semicondutors: Band Theory and Transport Properties, vol-ume1. Amsterdam: North-Holland,1982:178–197.
[112] Sipe J E, Shkrebtii A I. Second-order optical response in semiconductors. Phys. Rev. B,2000,61(8):5337–5352.
[113] Belkin M A, Kulakov T A, Ernst K H, et al. Sum-Frequency Vibrational Spectroscopy on ChiralLiquids: A Novel Technique to Probe Molecular Chirality. Phys. Rev. Lett.,2000,85(21):4474–4477.
[114] Wang J, Chen X, Clarke M L, et al. Detection of chiral sum frequency generation vibrationalspectra of proteins and peptides at interfaces in situ. Proc. Natl. Acad. Sci. U.S.A.,2005,102(14):4978–4983.
[115] Ji N, Ostroverkhov V, Belkin M, et al. Toward Chiral Sum-Frequency Spectroscopy. J. Am.Chem. Soc.,2006,128:8845–8848.
[116] Shen Y R. The Principles of Nonlinear Optics. New York: Wiley-Interscience,1984:30–51.
[117] Kuhrgin J B. Current induced second harmonic generation in semiconductors. Appl. Phys. Lett.,1995,67(8):1113–1115.
[118] Zhao H, Smirl A L, Driel H M. Temporally and spatially resolved ballistic pure spin transport.Phys. Rev. B,2007,75(7):075305.
[119] Hobbs P C D. Building Electro-Optical Systems. New Jersey: John Wiley,2009:56–79.
[120] Dresselhaus G. Spin-Orbit Coupling Efects in Zinc Blende Structures. Phys. Rev.,1955,100(2):580–586.
[121] Bychkov Y A, Rashba E I. Properties of a2D electron-gas with lifted spectral degeneracy.Pis’ma Zh. Eksp. Teor. Fiz.,1984,39:66.[Sov. Phys. JETP Lett.,39,78(1984)].
[122] Vlaminck V, Bailleul M. Current-Induced Spin-Wave Doppler Shift. Science,2008,322(5900):410–413.
[123] Semenov Y G, Kim K W. Phonon-Mediated Electron-Spin Phase Difusion in a Quantum Dot.Phys. Rev. Lett.,2004,92(2):026601.
[124] Khaetskii A V, Nazarov Y V. Spin relaxation in semiconductor quantum dots. Phys. Rev. B,2000,61(19):12639–12642.
[125] Khaetskii A V, Nazarov Y V. Spin-flip transitions between Zeeman sublevels in semiconductorquantum dots. Phys. Rev. B,2001,64(12):125316.
[126] Golovach V N, Khaetskii A, Loss D. Phonon-Induced Decay of the Electron Spin in QuantumDots. Phys. Rev. Lett.,2004,93(1):016601.
[127] Khaetskii A V, Loss D, Glazman L. Electron Spin Decoherence in Quantum Dots due to Inter-action with Nuclei. Phys. Rev. Lett.,2002,88(18):186802.
[128] Merkulov I A, Efros A L, Rosen M. Electron spin relaxation by nuclei in semiconductor quan-tum dots. Phys. Rev. B,2002,65(20):205309.
[129] Sousa R, Das Sarma S. Theory of nuclear-induced spectral difusion: Spin decoherence ofphosphorus donors in Si and GaAs quantum dots. Phys. Rev. B,2003,68(11):115322.
[130] Witzel W M, Sousa R, Das Sarma S. Quantum theory of spectral-difusion-induced electronspin decoherence. Phys. Rev. B,2005,72(16):161306.
[131] Yao W, Liu R B, Sham L J. Theory of electron spin decoherence by interacting nuclear spins ina quantum dot. Phys. Rev. B,2006,74(19):195301.
[132] Braun P F, Marie X, Lombez L, et al. Direct Observation of the Electron Spin RelaxationInduced by Nuclei in Quantum Dots. Phys. Rev. Lett.,2005,94(11):116601.
[133] Dutt M V G, Cheng J, Li B, et al. Stimulated and Spontaneous Optical Generation of ElectronSpin Coherence in Charged GaAs Quantum Dots. Phys. Rev. Lett.,2005,94(22):227403.
[134] Johnson A C, Petta J R, Taylor J M, et al. Triplet-singlet spin relaxation via nuclei in a doublequantum dot. Nature,2005,435:925.
[135] Tyryshkin A M, Lyon S A, Astashkin A V, et al. Electron spin relaxation times of phosphorusdonors in silicon. Phys. Rev. B,2003,68(19):193207.
[136] Abe E, Itoh K M, Isoya J, et al. Electron-spin phase relaxation of phosphorus donors in nuclear-spin-enriched silicon. Phys. Rev. B,2004,70(3):033204.
[137] Slichter C P. Principles of magnetic resonance.3rd ed ed., Berlin: Springer-Verlag,1992:45–67.
[138] Wu Y W, Li X Q, Steel D G, et al. Coherent optical control of semiconductor quantum dots forquantum information processing. Physica E,2004,25:242.
[139] Chen P, Piermarocchi C, Sham L J, et al. Theory of quantum optical control of a single spin ina quantum dot. Phys. Rev. B,2004,69(7):075320.
[140] Kubo R. Note on the Stochastic Theory of Resonance Absorption. J. Phys. Soc. Jpn.,1954,9:935.
[141] Kubo R. A mathematical model for the narrowing of spectral lines by exchange or motion. J.Phys. Soc. Jpn.,1954,9:316.
[142] Klauder J R, Anderson P W. Spectral Difusion Decay in Spin Resonance Experiments. Phys.Rev.,1962,125(3):912–932.
[143] Kubo R. Stochastic Processes in Chemical Physics. New York: Interscience,1969:20–65.
[144] Hahn E L. Spin Echoes. Phys. Rev.,1950,80(4):580–594.
[145] Liu R B, Economou S E, Sham L J, et al. Theory of nonlinear optical spectroscopy of electronspin coherence in quantum dots. Phys. Rev. B,2007,75(8):085322.
[146] Loring R F, Mukamel S. Unified theory of photon echoes: the passage from inhomogeneous tohomogeneous line broadening. Chem. Phys. Lett.,1985,114:426.
[147] Harris S E, Field J E, Imamog lu A. Nonlinear optical processes using electromagnetically in-duced transparency. Phys. Rev. Lett.,1990,64(10):1107–1110.
[148] Gupta J A, Knobel R, Samarth N, et al. Ultrafast Manipulation of Electron Spin Coherence.Science,2001,292(5526):2458–2461.
[149] Wu Y, Kim E D, Xu X, et al. Selective Optical Control of Electron Spin Coherence in SinglyCharged GaAs-Al0.3Ga0.7As Quantum Dots. Phys. Rev. Lett.,2007,99(9):097402.
[150] Berezovsky J, Mikkelsen M H, Stoltz N G, et al. Picosecond Coherent Optical Manipulation ofa Single Electron Spin in a Quantum Dot. Science,2008,320(5874):349–352.
[151] Clark S M, Fu K M C, Zhang Q, et al. Ultrafast Optical Spin Echo for Electron Spins inSemiconductors. Phys. Rev. Lett.,2009,102(24):247601.
[152] Greilich A, Economou S E, Spatzek S, et al. Ultrafast optical rotations of electron spins inquantum dots. Nat. Phys.,2009,5:262.
[153] Phelps C, Sweeney T, Cox R T, et al. Ultrafast Coherent Electron Spin Flip in a Modulation-Doped CdTe Quantum Well. Phys. Rev. Lett.,2009,102(23):237402.
[154] Press D, Greve K D, McMahon P L, et al. Ultrafast optical spin echo in a single quantum dot.Nat. Photon.,2010,4:367.
[155] Lindberg M, Binder R, Koch S W. Theory of the semiconductor photon echo. Phys. Rev. A,1992,45(3):1865–1875.
[156] Kubo R. The fluctuation-dissipation theorem. Rep. Prog. Phys.,1966,29:255.
[157] Economou S E, Liu R B, Sham L J, et al. Unified theory of consequences of spontaneousemission in a Λ system. Phys. Rev. B,2005,71(19):195327.
[158] Stievater T H, Li X, Steel D G, et al. Rabi Oscillations of Excitons in Single Quantum Dots.Phys. Rev. Lett.,2001,87(13):133603.
[159] Bonadeo N H, Chen G, Gammon D, et al. Nonlinear Nano-Optics: Probing One Exciton at aTime. Phys. Rev. Lett.,1998,81(13):2759–2762.
[160] Li R, Wang J, Qi X L, et al. Dynamical axion field in topological magnetic insulators. Nat.Phys.,2010,6:284.
[161] Wang J, Li R, Zhang S C, et al. Topological Magnetic Insulators with Corundum Structure.Phys. Rev. Lett.,2011,106(12):126403.
[162] Fu L, Kane C L. Time reversal polarization and a Z2adiabatic spin pump. Phys. Rev. B,2006,74(19):195312.
[163] Fukui T, Fujiwara T, Hatsugai Y. Quantum Spin Hall Efect in Three Dimensional Materials:Lattice Computation of Z2Topological Invariants and Its Application to Bi and Sb. J. Phys. Soc.Jpn.,2007,75:053702.
[164] Fukui T, Fujiwara T, Hatsugai Y. Topological Meaning of Z2Numbers in Time Reversal Invari-ant Systems. J. Phys. Soc. Jpn.,2008,77:123705.
[165] Qi X L, Hughes T L, Zhang S C. Topological field theory of time-reversal invariant insulators.Phys. Rev. B,2008,78(19):195424.
[166] Wang Z, Qi X L, Zhang S C. Equivalent topological invariants of topological insulators. New J.Phys.,2010,12:065007.
[167] Liu C X, Qi X L, Zhang H, et al. Model Hamiltonian for topological insulators. Phys. Rev. B,2010,82(4):045122.
[168] Maiani L, Petronzio R, Zavattini E. Efects of nearly massless, spin-zero particles on lightporpagation in a magnetic field. Phys. Lett. B,1986,175:359.
[169] Mills D L, Burstein E. Polaritons: the electromagnetic modes of media. Rep. Prog. Phys.,1974,37:817.
[170] Rafelt G, Stodolsky L. Mixing of the photon with low-mass particles. Phys. Rev. D,1988,37:1237.
[171] Cameron R, Cantatore G, Melissinos A C, et al. Search for nearly massless, weakly coupledparticles by optical techniques. Phys. Rev. D,1993,47:3707.
[172] Lohndorf M, Moreland J, Kabos P, et al. Microcantilever torque magnetometry of thin magneticfilms. J. Appl. Phys.,2000,87:5995.
[173] Mamin H J, Budakian R, Chui B W, et al. Detection and manipulation polarization in small spinensembles. Phys. Rev. Lett.,2003,91:207604.
[174] Budakian R, Mamin H J, Chui B W, et al. Creating order from random fluctuations in small spinensembles. Science,2005,307:408.
[175] Raghu S, Qi X L, Honerkamp C, et al. Topological Mott Insulators. Phys. Rev. Lett.,2008,100(15):156401.
[176] Shitade A, Katsura H, KunesˇJ, et al. Quantum Spin Hall Efect in a Transition Metal OxideNa2IrO3. Phys. Rev. Lett.,2009,102(25):256403.
[177] Guo H M, Franz M. Three-Dimensional Topological Insulators on the Pyrochlore Lattice. Phys.Rev. Lett.,2009,103(20):206805.
[178] Pesin D, Balents L. Mott physics and band topology in materials with strong spin-orbit interac-tion. Nat. Phys.,2010,6:376.
[179] Prewitt C T, Shannon R D, Rogers D B, et al. The C rare earth oxide-corundum transition andcrystal chemistry of oxides having the corundum structure. Inorg. Chem.,1969,8:1985.
[180] Nebenzahl I, Weger M. Band structure of the3d-t2gsub-shell of V2O3and Ti2O3in the tight-binding approximation. Phil. Mag.,1971,24:1119.
[181] Harrison W A. Elementary Electronic Structure. Singapore: World Scientific,1999:67–87.
[182] Kim B J, Jin H, Moon S J, et al. Novel Jef=1/2Mott State Induced by Relativistic Spin-OrbitCoupling in Sr2IrO4. Phys. Rev. Lett.,2008,101(7):076402.
[183] Kim B J, Ohsumi H, Komesu T, et al. Phase-Sensitive Observation of a Spin-Orbital Mott Statein Sr2IrO4. Science,2009,323(5919):1329–1332.
[184] Brunel M, Bergevin F D. Difrraction of X-rays by Magnetic Materials. II. Measurements onAntiferromagnetic Fe2O3. Acta. Cryst.,1987, A37:324.
[185] Morrish A H. Canted Antiferromagnetism: Hermatite. Singapore: World Scientific,1994:57–100.
[186] Catti M, Valerio G, Dovesi R. Theoretical study of electronic, magnetic, and structural propertiesof α-Fe2O3(hematite). Phys. Rev. B,1995,51(12):7441–7450.
[187] Qi X L, Li R, Zang J, et al. Inducing a Magnetic Monopole with Topological Surface States.Science,2009,323(5918):1184–1187.
[188] Fu L, Kane C L. Superconducting Proximity Efect and Majorana Fermions at the Surface of aTopological Insulator. Phys. Rev. Lett.,2008,100(9):096407.
[189] Qi X L, Hughes T L, Raghu S, et al. Time-Reversal-Invariant Topological Superconductors andSuperfluids in Two and Three Dimensions. Phys. Rev. Lett.,2009,102(18):187001.
[190] Kuroda K, Arita M, Miyamoto K, et al. Hexagonally Deformed Fermi Surface of the3D Topo-logical Insulator Bi2Se3. Phys. Rev. Lett.,2010,105(7):076802.
[191] Zhang Y, He K, Chang C Z, et al. Crossover of the three-dimensional topological insulatorBi2Se3to the two-dimensional limit. Nat. Phys.,2010,6:584–588.
[192] Cheng P, Song C, Zhang T, et al. Landau Quantization of Topological Surface States in Bi2Se3.Phys. Rev. Lett.,2010,105(7):076801.
[193] Hanaguri T, Igarashi K, Kawamura M, et al. Momentum-resolved Landau-level spectroscopy ofDirac surface state in Bi2Se3. Phys. Rev. B,2010,82(8):081305.
[194] Wang J, Li W, Deng P, et al. Power laws and STM image of standing wave of the topologicalsurface states. Submitted to Phys. Rev. Lett., preprint at arXiv: cond-mat/1105.1957.
[195] Lu H Z, Shan W Y, Yao W, et al. Massive Dirac fermions and spin physics in an ultrathin filmof topological insulator. Phys. Rev. B,2010,81(11):115407.
[196] Roth L M, Zeiger H J, Kaplan T A. Generalization of the Ruderman-Kittel-Kasuya-YosidaInteraction for Nonspherical Fermi Surfaces. Phys. Rev.,1966,149(2):519–525.
[197] Crommie M F, Lutz C P, Eigler D M. Imaging standing waves in a two-dimensional electrongas. Nature,1993,363:524–527.
[198] Lee W C, Wu C, Arovas D P, et al. Quasiparticle interference on the surface of the topologicalinsulator Bi2Te3. Phys. Rev. B,2009,80(24):245439.
[199] Zhou X, Fang C, Tsai W F, et al. Theory of quasiparticle scattering in a two-dimensional systemof helical Dirac fermions: Surface band structure of a three-dimensional topological insulator.Phys. Rev. B,2009,80(24):245317.
[200] Wang Q H, Wang D, Zhang F C. Electronic structure near an impurity and terrace on the surfaceof a three-dimensional topological insulator. Phys. Rev. B,2010,81(3):035104.
[201] Okada Y, Dhital C, Zhou W, et al. Direct Observation of Broken Time-Reversal Symmetry on theSurface of a Magnetically Doped Topological Insulator. Phys. Rev. Lett.,2011,106(20):206805.
[202] Linder J, Tanaka Y, Yokoyama T, et al. Unconventional Superconductivity on a TopologicalInsulator. Phys. Rev. Lett.,2010,104(6):067001.
[203] Seradjeh B, Moore J E, Franz M. Exciton Condensation and Charge Fractionalization in aTopological Insulator Film. Phys. Rev. Lett.,2009,103(6):066402.
[204] Chen Y L, Chu J H, Analytis J G, et al. Massive Dirac Fermion on the Surface of a MagneticallyDoped Topological Insulator. Science,2010,329(5992):659–662.
[205] Li Y Y, Wang G, Zhu X G, et al. Intrinsic Topological Insulator Bi2Te3Thin Films on Si andTheir Thickness Limit. Advanced Materials,2010,22(36):4002–4007.
[206] Ren Z, Taskin A A, Sasaki S, et al. Large bulk resistivity and surface quantum oscillations inthe topological insulator Bi2Te2Se. Phys. Rev. B,2010,82(24):241306.
[207] Liu M, Chang C Z, Zhang Z, et al. Electron interaction-driven insulating ground state in Bi2Se3topological insulators in the two-dimensional limit. Phys. Rev. B,2011,83(16):165440.
[2]Z utic′I, Fabian J, Das Sarma S. Spintronics: Fundamentals and applications. Rev. Mod. Phys.,2004,76(2):323–410.
[3] Awschalom D D, Flatte M E. Challenges for semiconductor spintronics. Nat. Phys.,2007,3:153.
[4] Awschalom D D, Loss D, Samarth N. Semiconductor Spintronics and Quantum Computation.Berlin: Springer,2002.
[5] Baibich M N, Broto J M, Fert A, et al. Giant Magnetoresistance of (001)Fe/(001)Cr MagneticSuperlattices. Phys. Rev. Lett.,1988,61(21):2472–2475.
[6] Datta S, Das B. Electronic analog of the electro-optic modulator. Appl. Phys. Lett.,1990,56:665.
[7] Meier F, Zakharchenya B P. Optical Orientation. Amsterdam: North-Holland,1984:12–71.
[8] Bhat R D R, Sipe J E. Optically Injected Spin Currents in Semiconductors. Phys. Rev. Lett.,2000,85(25):5432–5435.
[9] Schmidt G, Ferrand D, Molenkamp L W, et al. Fundamental obstacle for electrical spin injectionfrom a ferromagnetic metal into a difusive semiconductor. Phys. Rev. B,2000,62(8):R4790–R4793.
[10] Rashba E I. Theory of electrical spin injection: Tunnel contacts as a solution of the conductivitymismatch problem. Phys. Rev. B,2000,62(24):R16267–R16270.
[11] Zhu H J, Ramsteiner M, Kostial H, et al. Room-Temperature Spin Injection from Fe into GaAs.Phys. Rev. Lett.,2001,87(1):016601.
[12] Hirsch J E. Spin Hall Efect. Phys. Rev. Lett.,1999,83(9):1834–1837.
[13] Murakami S, Nagaosa N, Zhang S C. Dissipationless Quantum Spin Current at Room Temper-ature. Science,2003,301(5638):1348–1351.
[14] Sinova J, Culcer D, Niu Q, et al. Universal Intrinsic Spin Hall Efect. Phys. Rev. Lett.,2004,92(12):126603.
[15] Dyakonov M I, Perel V I. Current-induced spin orientation of electrons in semiconductors.Phys. Lett. A,1971,35:459.
[16] Kato Y, Myers R C, Gossard A C, et al. Coherent spin manipulation without magnetic fields instrained semiconductors. Nature,2004,427:50.
[17] Silov A Y, Blajnov P A, Wolter J H, et al. Current-induced spin polarization at a single hetero-junction. Appl. Phys. Lett.,2004,85:5929.
[18] Hall E. On a New Action of the Magnet on Electric Currents. Am. J. Math.,1879,2:287.
[19] Inoue J, Ohno H. Taking the Hall Efect for a Spin. Science,2005,309(5743):2004–2005.
[20] Wunderlich J, Park B G, Irvine A C, et al. Spin Hall Efect Transistor. Science,2010,330(6012):1801–1804.
[21] Qi X L, Zhang S C. The quantum spin Hall efect and topological insulators. Phys. Tod.,2010,63(1):33–38.
[22] Moore J E. The birth of topological insulators. Nature,2010,464:194–198.
[23] Hasan M Z, Kane C L. Colloquium: Topological insulators. Rev. Mod. Phys.,2010,82(4):3045–3067.
[24] Wang J, Zhu B F, Liu R B. Proposal for Direct Measurement of a Pure Spin Current by aPolarized Light Beam. Phys. Rev. Lett.,2008,100(8):086603.
[25] Wang J, Zhu B F, Liu R B. Second-Order Nonlinear Optical Efects of Spin Currents. Phys.Rev. Lett.,2010,104(25):256601.
[26] Weraka L K, Zhao H. Observation of second-harmonic generation induced by pure spin currents.Nat. Phys.,2010,6:875.
[27] Cirac J I, Zoller P. A scalable quantum computer with ions in an array of microtraps. Nature,2000,404:579.
[28] Kielpinski D, Monroe C, Wineland D J. Architecture for a large-scale ion-trap quantum com-puter. Nature,2002,417:709.
[29] Yamamoto T, Pashkin Y A, Astafiev O, et al. Demonstration of conditional gate operation usingsuperconducting charge qubits. Nature,2003,425:941.
[30] O’Brien J L, Pryde G J, White A G, et al. Demonstration of an all-optical quantum controlled-NOT gate. Nature,2003,426:264.
[31] Vandersypen L M K, Stefen M, Breyta G, et al. Experimental realization of Shor’s quantumfactoring algorithm using nuclear magnetic resonance. Nature,2001,414:883.
[32] Liu R B, Yao W, Sham L J. Quantum computation by optical control of electron spins. Adv.Phys.,2010,59:703.
[33] Petta J R, Johnson A C, Taylor J M, et al. Coherent Manipulation of Coupled Electron Spins inSemiconductor Quantum Dots. Science,2005,309(5744):2180–2184.
[34] Greilich A, Yakovlev D R, Shabaev A, et al. Mode Locking of Electron Spin Coherences inSingly Charged Quantum Dots. Science,2006,313(5785):341–345.
[35] Bracker A S, Stinaf E A, Gammon D, et al. Optical Pumping of the Electronic and NuclearSpin of Single Charge-Tunable Quantum Dots. Phys. Rev. Lett.,2005,94(4):047402.
[36] Reilly D J, Taylor J M, Petta J R, et al. Suppressing Spin Qubit Dephasing by Nuclear StatePreparation. Science,2008,321(5890):817–821.
[37] Jelezko F, Gaebel T, Popa I, et al. Observation of Coherent Oscillation of a Single NuclearSpin and Realization of a Two-Qubit Conditional Quantum Gate. Phys. Rev. Lett.,2004,93(13):130501.
[38] Taylor J M, Marcus C M, Lukin M D. Long-Lived Memory for Mesoscopic Quantum Bits.Phys. Rev. Lett.,2003,90(20):206803.
[39] Uhrig G S. Keeping a Quantum Bit Alive by Optimized π-Pulse Sequences. Phys. Rev. Lett.,2007,98(10):100504.
[40] Yang W, Liu R B. Universality of Uhrig Dynamical Decoupling for Suppressing Qubit PureDephasing and Relaxation. Phys. Rev. Lett.,2008,101(18):180403.
[41] Greilich A, Shabaev A, Yakovlev D R, et al. Nuclei-Induced Frequency Focusing of ElectronSpin Coherence. Science,2007,317(5846):1896–1899.
[42] Xu X, Yao W, Sun B, et al. Optically controlled locking of the nuclear field via coherent dark-state spectroscopy. Nature,2009,459:1105.
[43] Sham L J, Rice T M. Many-Particle Derivation of the Efective-Mass Equation for the WannierExciton. Phys. Rev.,1966,144(2):708–714.
[44] Li X, Wu Y, Steel D, et al. An All-Optical Quantum Gate in a Semiconductor Quantum Dot.Science,2003,301(5634):809–811.
[45] Wang J, Liu R B, Zhu B F, et al. Coherent spin control by electromagnetic vacuum fluctuations.Phys. Rev. A,2011,83(5):053833.
[46] Anderson P W. Basic Notions of Condensed Matter Physics. Westview Press,1997:57–87.
[47] Landau L D, Lifshitz E M. Statistical Physics. Oxford: Pergamon Press,1980:1–10.
[48] Thouless D J, Kohmoto M, Nightingale M P, et al. Quantized Hall Conductance in a Two-Dimensional Periodic Potential. Phys. Rev. Lett.,1982,49(6):405–408.
[49] Wen X G. Topological orders and Edge excitations in FQH states. Adv. Phys.,1995,44:405.
[50] Kane C L, Mele E J. Quantum Spin Hall Efect in Graphene. Phys. Rev. Lett.,2005,95(22):226801.
[51] Kane C L, Mele E J. Z2Topological Order and the Quantum Spin Hall Efect. Phys. Rev. Lett.,2005,95(14):146802.
[52] Bernevig B A, Zhang S C. Quantum Spin Hall Efect. Phys. Rev. Lett.,2006,96(10):106802.
[53] Bernevig B A, Hughes T L, Zhang S C. Quantum Spin Hall Efect and Topological PhaseTransition in HgTe Quantum Wells. Science,2006,314(5806):1757–1761.
[54] Fu L, Kane C L, Mele E J. Topological Insulators in Three Dimensions. Phys. Rev. Lett.,2007,98(10):106803.
[55] Fu L, Kane C L. Topological insulators with inversion symmetry. Phys. Rev. B,2007,76(4):045302.
[56] Moore J E, Balents L. Topological invariants of time-reversal-invariant band structures. Phys.Rev. B,2007,75(12):121306.
[57] Roy R. Z2classification of quantum spin Hall systems: An approach using time-reversal invari-ance. Phys. Rev. B,2009,79(19):195321.
[58] Ko¨nig M, Wiedmann S, Bru¨ne C, et al. Quantum Spin Hall Insulator State in HgTe QuantumWells. Science,2007,318(5851):766–770.
[59] Hsieh D, Qian D, Wray L, et al. A topological Dirac insulator in a quantum spin Hall phase.Nature,2008,452:970–974.
[60] Xia Y, Qian D, Hsieh D, et al. Observation of a large-gap topological-insulator class with asingle Dirac cone on the surface. Nat. Phys.,2009,5:398–402.
[61] Zhang H, Liu C X, Qi X L, et al. Topological insulators in Bi2Se3, Bi2Te3and Sb2Te3with asingle Dirac cone on the surface. Nat. Phys.,2009,5(6):438–442.
[62] Klitzing K v, Dorda G, Pepper M. New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance. Phys. Rev. Lett.,1980,45(6):494–497.
[63] Laughlin R B. Quantized Hall conductivity in two dimensions. Phys. Rev. B,1981,23(10):5632–5633.
[64] Bu¨ttiker M. Four-Terminal Phase-Coherent Conductance. Phys. Rev. Lett.,1986,57(14):1761–1764.
[65] Hatsugai Y. Chern number and edge states in the integer quantum Hall efect. Phys. Rev. Lett.,1993,71(22):3697–3700.
[66] Datta S. Electronic Transport in Mesoscopic Systems. New York: Cambridge University,1989:78–99.
[67] Redlich A N. Gauge Noninvariance and Parity Nonconservation of Three-DimensionalFermions. Phys. Rev. Lett.,1984,52(1):18–21.
[68] Semenof G W. Condensed-Matter Simulation of a Three-Dimensional Anomaly. Phys. Rev.Lett.,1984,53(26):2449–2452.
[69] Wu C, Bernevig B A, Zhang S C. Helical Liquid and the Edge of Quantum Spin Hall Systems.Phys. Rev. Lett.,2006,96(10):106401.
[70] Xu C, Moore J E. Stability of the quantum spin Hall efect: Efects of interactions, disorder, andZ2topology. Phys. Rev. B,2006,73(4):045322.
[71] Huertas-Hernando D, Guinea F, Brataas A. Spin-orbit coupling in curved graphene, fullerenes,nanotubes, and nanotube caps. Phys. Rev. B,2006,74(15):155426.
[72] Min H, Hill J E, Sinitsyn N A, et al. Intrinsic and Rashba spin-orbit interactions in graphenesheets. Phys. Rev. B,2006,74(16):165310.
[73] Yao Y, Ye F, Qi X L, et al. Spin-orbit gap of graphene: First-principles calculations. Phys. Rev.B,2007,75(4):041401.
[74] Roth A, Brüne C, Buhmann H, et al. Nonlocal Transport in the Quantum Spin Hall State.Science,2009,325(5938):294–297.
[75] Hsieh D, Xia Y, Wray L, et al. Observation of Unconventional Quantum Spin Textures inTopological Insulators. Science,2009,323(5916):919–922.
[76] Hsieh D, Xia Y, Qian D, et al. A tunable topological insulator in the spin helical Dirac transportregime. Nature,2009,460:1101–1106.
[77] Chen Y L, Analytis J G, Chu J H, et al. Experimental Realization of a Three-DimensionalTopological Insulator Bi2Te3. Science,2009,325(5937):178–181.
[78] Fu L. Hexagonal Warping Efects in the Surface States of the Topological Insulator Bi2Te3.Phys. Rev. Lett.,2009,103(26):266801.
[79] M Zahid Hasan H L, Bansil A. Warping the cone on a Topological Insulator. Physics,2009,2:108.
[80] Zhang T, Cheng P, Chen X, et al. Experimental Demonstration of Topological Surface StatesProtected by Time-Reversal Symmetry. Phys. Rev. Lett.,2009,103(26):266803.
[81] Alpichshev Z, Analytis J G, Chu J H, et al. STM Imaging of Electronic Waves on the Surfaceof Bi2Te3: Topologically Protected Surface States and Hexagonal Warping Efects. Phys. Rev.Lett.,2010,104(1):016401.
[82] Hsieh D, Xia Y, Qian D, et al. Observation of Time-Reversal-Protected Single-Dirac-ConeTopological-Insulator States in Bi2Te3and Sb2Te3. Phys. Rev. Lett.,2009,103(14):146401.
[83] Wang G, Zhu X, Wen J, et al. Atomically smooth ultrathin films of topological insulator Sb2Te3.Nano Research,2010,3:874–880.
[84] Chadov S, Qi X L, Ku¨bler J, et al. Tunable multifunctional topological insulators in ternaryHeusler compounds. Nat. Mat.,2010,9:541.
[85] Lin H, Wray L A, Xia Y, et al. Half-Heusler ternary compounds as new multifunctional experi-mental platforms for topological quantum phenomena. Nat. Mat.,2010,9:546.
[86] Sato T, Segawa K, Guo H, et al. Direct Evidence for the Dirac-Cone Topological Surface Statesin the Ternary Chalcogenide TlBiSe2. Phys. Rev. Lett.,2010,105(13):136802.
[87] Chen Y L, Liu Z K, Analytis J G, et al. Single Dirac Cone Topological Surface State and UnusualThermoelectric Property of Compounds from a New Topological Insulator Family. Phys. Rev.Lett.,2010,105(26):266401.
[88] Nielsen H B, Ninomiya N. Absence of nretrinos on a lattice (I). Proof by homotopy theory. Nul.Phys. B,1981,185:20.
[89] Nielsen H B, Ninomiya N. Absence of nretrinos on a lattice (II). Intuitive topological proof.Nul. Phys. B,1981,193:173.
[90] Bousso R. The holographic principle. Rev. Mod. Phys.,2002,74(3):825–874.
[91] Sharma P. How to Create a Spin Current. Science,2005,307(5709):531–533.
[92] Shi J, Zhang P, Xiao D, et al. Proper Definition of Spin Current in Spin-Orbit Coupled Systems.Phys. Rev. Lett.,2006,96(7):076604.
[93] Kikkawa J M, Awschalom D D. Lateral drag of spin coherence in gallium arsenide. Nature,1999,397:139.
[94] Stephens J, Berezovsky J, McGuire J P, et al. Spin Accumulation in Forward-BiasedMnAs/GaAs Schottky Diodes. Phys. Rev. Lett.,2004,93(9):097602.
[95] Crooker S A, Furis M, Lou X, et al. Imaging Spin Transport in Lateral Ferromag-net/Semiconductor Structures. Science,2005,309(5744):2191–2195.
[96] Zhang S. Spin Hall Efect in the Presence of Spin Difusion. Phys. Rev. Lett.,2000,85(2):393–396.
[97] Kato Y K, Myers R C, Gossard A C, et al. Observation of the Spin Hall Efect in Semiconduc-tors. Science,2004,306(5703):1910–1913.
[98] Wunderlich J, Kaestner B, Sinova J, et al. Experimental Observation of the Spin-Hall Efectin a Two-Dimensional Spin-Orbit Coupled Semiconductor System. Phys. Rev. Lett.,2005,94(4):047204.
[99] Zhao H, Loren E J, Driel H M, et al. Coherence Control of Hall Charge and Spin Currents. Phys.Rev. Lett.,2006,96(24):246601.
[100] Valenzuela S O, Tinkham M. Direct electronic measurement of the spin Hall efect. Nature,2006,442:176.
[101] Kimura T, Otani Y, Sato T, et al. Room-Temperature Reversible Spin Hall Efect. Phys. Rev.Lett.,2007,98(15):156601.
[102] Seki T, Hasegawa Y, Mitani S, et al. Giant spin Hall efect in perpendicularly spin-polarizedFePt/Au devices. Nat. Mat.,2008,7:125.
[103] Cui X D, Shen S Q, Li J, et al. Observation of electric current induced by optically injected spincurrent. Appl. Phys. Lett.,2007,90(24):242115.
[104] Ganichev S D, Bel’kov1V V, Tarasenko S A, et al. Zero-bias spin separation. Nat. Phys.,2006,2:609.
[105] Ganichev S D, Danilov S N, Bel’kov V V, et al. Pure spin currents induced by spin-dependentscattering processes in SiGe quantum well structures. Phys. Rev. B,2007,75(15):155317.
[106] Coleman S, Wess J, Zumino B. Structure of Phenomenological Lagrangians. I. Phys. Rev.,1969,177(5):2239–2247.
[107] Callan C G, Coleman S, Wess J, et al. Structure of Phenomenological Lagrangians. II. Phys.Rev.,1969,177(5):2247–2250.
[108] Jones R C. A New Calculus for the Treatment of Optical Systems. J. Opt. Soc. Am.,1941,31:488.
[109] Zvezdin A K, Kotov V A. Modern Magnetooptics and Magnetooptical Materials. New York:Taylor and Francis Group,1997:1–25.
[110] Yu P Y, Cardona M. Fundamentals of Semiconductors: Physics and Material Properties.3rd eded., Berlin: Springer-Verlag,2005:63–77.
[111] Paul W, Moss T S. Handbook on Semicondutors: Band Theory and Transport Properties, vol-ume1. Amsterdam: North-Holland,1982:178–197.
[112] Sipe J E, Shkrebtii A I. Second-order optical response in semiconductors. Phys. Rev. B,2000,61(8):5337–5352.
[113] Belkin M A, Kulakov T A, Ernst K H, et al. Sum-Frequency Vibrational Spectroscopy on ChiralLiquids: A Novel Technique to Probe Molecular Chirality. Phys. Rev. Lett.,2000,85(21):4474–4477.
[114] Wang J, Chen X, Clarke M L, et al. Detection of chiral sum frequency generation vibrationalspectra of proteins and peptides at interfaces in situ. Proc. Natl. Acad. Sci. U.S.A.,2005,102(14):4978–4983.
[115] Ji N, Ostroverkhov V, Belkin M, et al. Toward Chiral Sum-Frequency Spectroscopy. J. Am.Chem. Soc.,2006,128:8845–8848.
[116] Shen Y R. The Principles of Nonlinear Optics. New York: Wiley-Interscience,1984:30–51.
[117] Kuhrgin J B. Current induced second harmonic generation in semiconductors. Appl. Phys. Lett.,1995,67(8):1113–1115.
[118] Zhao H, Smirl A L, Driel H M. Temporally and spatially resolved ballistic pure spin transport.Phys. Rev. B,2007,75(7):075305.
[119] Hobbs P C D. Building Electro-Optical Systems. New Jersey: John Wiley,2009:56–79.
[120] Dresselhaus G. Spin-Orbit Coupling Efects in Zinc Blende Structures. Phys. Rev.,1955,100(2):580–586.
[121] Bychkov Y A, Rashba E I. Properties of a2D electron-gas with lifted spectral degeneracy.Pis’ma Zh. Eksp. Teor. Fiz.,1984,39:66.[Sov. Phys. JETP Lett.,39,78(1984)].
[122] Vlaminck V, Bailleul M. Current-Induced Spin-Wave Doppler Shift. Science,2008,322(5900):410–413.
[123] Semenov Y G, Kim K W. Phonon-Mediated Electron-Spin Phase Difusion in a Quantum Dot.Phys. Rev. Lett.,2004,92(2):026601.
[124] Khaetskii A V, Nazarov Y V. Spin relaxation in semiconductor quantum dots. Phys. Rev. B,2000,61(19):12639–12642.
[125] Khaetskii A V, Nazarov Y V. Spin-flip transitions between Zeeman sublevels in semiconductorquantum dots. Phys. Rev. B,2001,64(12):125316.
[126] Golovach V N, Khaetskii A, Loss D. Phonon-Induced Decay of the Electron Spin in QuantumDots. Phys. Rev. Lett.,2004,93(1):016601.
[127] Khaetskii A V, Loss D, Glazman L. Electron Spin Decoherence in Quantum Dots due to Inter-action with Nuclei. Phys. Rev. Lett.,2002,88(18):186802.
[128] Merkulov I A, Efros A L, Rosen M. Electron spin relaxation by nuclei in semiconductor quan-tum dots. Phys. Rev. B,2002,65(20):205309.
[129] Sousa R, Das Sarma S. Theory of nuclear-induced spectral difusion: Spin decoherence ofphosphorus donors in Si and GaAs quantum dots. Phys. Rev. B,2003,68(11):115322.
[130] Witzel W M, Sousa R, Das Sarma S. Quantum theory of spectral-difusion-induced electronspin decoherence. Phys. Rev. B,2005,72(16):161306.
[131] Yao W, Liu R B, Sham L J. Theory of electron spin decoherence by interacting nuclear spins ina quantum dot. Phys. Rev. B,2006,74(19):195301.
[132] Braun P F, Marie X, Lombez L, et al. Direct Observation of the Electron Spin RelaxationInduced by Nuclei in Quantum Dots. Phys. Rev. Lett.,2005,94(11):116601.
[133] Dutt M V G, Cheng J, Li B, et al. Stimulated and Spontaneous Optical Generation of ElectronSpin Coherence in Charged GaAs Quantum Dots. Phys. Rev. Lett.,2005,94(22):227403.
[134] Johnson A C, Petta J R, Taylor J M, et al. Triplet-singlet spin relaxation via nuclei in a doublequantum dot. Nature,2005,435:925.
[135] Tyryshkin A M, Lyon S A, Astashkin A V, et al. Electron spin relaxation times of phosphorusdonors in silicon. Phys. Rev. B,2003,68(19):193207.
[136] Abe E, Itoh K M, Isoya J, et al. Electron-spin phase relaxation of phosphorus donors in nuclear-spin-enriched silicon. Phys. Rev. B,2004,70(3):033204.
[137] Slichter C P. Principles of magnetic resonance.3rd ed ed., Berlin: Springer-Verlag,1992:45–67.
[138] Wu Y W, Li X Q, Steel D G, et al. Coherent optical control of semiconductor quantum dots forquantum information processing. Physica E,2004,25:242.
[139] Chen P, Piermarocchi C, Sham L J, et al. Theory of quantum optical control of a single spin ina quantum dot. Phys. Rev. B,2004,69(7):075320.
[140] Kubo R. Note on the Stochastic Theory of Resonance Absorption. J. Phys. Soc. Jpn.,1954,9:935.
[141] Kubo R. A mathematical model for the narrowing of spectral lines by exchange or motion. J.Phys. Soc. Jpn.,1954,9:316.
[142] Klauder J R, Anderson P W. Spectral Difusion Decay in Spin Resonance Experiments. Phys.Rev.,1962,125(3):912–932.
[143] Kubo R. Stochastic Processes in Chemical Physics. New York: Interscience,1969:20–65.
[144] Hahn E L. Spin Echoes. Phys. Rev.,1950,80(4):580–594.
[145] Liu R B, Economou S E, Sham L J, et al. Theory of nonlinear optical spectroscopy of electronspin coherence in quantum dots. Phys. Rev. B,2007,75(8):085322.
[146] Loring R F, Mukamel S. Unified theory of photon echoes: the passage from inhomogeneous tohomogeneous line broadening. Chem. Phys. Lett.,1985,114:426.
[147] Harris S E, Field J E, Imamog lu A. Nonlinear optical processes using electromagnetically in-duced transparency. Phys. Rev. Lett.,1990,64(10):1107–1110.
[148] Gupta J A, Knobel R, Samarth N, et al. Ultrafast Manipulation of Electron Spin Coherence.Science,2001,292(5526):2458–2461.
[149] Wu Y, Kim E D, Xu X, et al. Selective Optical Control of Electron Spin Coherence in SinglyCharged GaAs-Al0.3Ga0.7As Quantum Dots. Phys. Rev. Lett.,2007,99(9):097402.
[150] Berezovsky J, Mikkelsen M H, Stoltz N G, et al. Picosecond Coherent Optical Manipulation ofa Single Electron Spin in a Quantum Dot. Science,2008,320(5874):349–352.
[151] Clark S M, Fu K M C, Zhang Q, et al. Ultrafast Optical Spin Echo for Electron Spins inSemiconductors. Phys. Rev. Lett.,2009,102(24):247601.
[152] Greilich A, Economou S E, Spatzek S, et al. Ultrafast optical rotations of electron spins inquantum dots. Nat. Phys.,2009,5:262.
[153] Phelps C, Sweeney T, Cox R T, et al. Ultrafast Coherent Electron Spin Flip in a Modulation-Doped CdTe Quantum Well. Phys. Rev. Lett.,2009,102(23):237402.
[154] Press D, Greve K D, McMahon P L, et al. Ultrafast optical spin echo in a single quantum dot.Nat. Photon.,2010,4:367.
[155] Lindberg M, Binder R, Koch S W. Theory of the semiconductor photon echo. Phys. Rev. A,1992,45(3):1865–1875.
[156] Kubo R. The fluctuation-dissipation theorem. Rep. Prog. Phys.,1966,29:255.
[157] Economou S E, Liu R B, Sham L J, et al. Unified theory of consequences of spontaneousemission in a Λ system. Phys. Rev. B,2005,71(19):195327.
[158] Stievater T H, Li X, Steel D G, et al. Rabi Oscillations of Excitons in Single Quantum Dots.Phys. Rev. Lett.,2001,87(13):133603.
[159] Bonadeo N H, Chen G, Gammon D, et al. Nonlinear Nano-Optics: Probing One Exciton at aTime. Phys. Rev. Lett.,1998,81(13):2759–2762.
[160] Li R, Wang J, Qi X L, et al. Dynamical axion field in topological magnetic insulators. Nat.Phys.,2010,6:284.
[161] Wang J, Li R, Zhang S C, et al. Topological Magnetic Insulators with Corundum Structure.Phys. Rev. Lett.,2011,106(12):126403.
[162] Fu L, Kane C L. Time reversal polarization and a Z2adiabatic spin pump. Phys. Rev. B,2006,74(19):195312.
[163] Fukui T, Fujiwara T, Hatsugai Y. Quantum Spin Hall Efect in Three Dimensional Materials:Lattice Computation of Z2Topological Invariants and Its Application to Bi and Sb. J. Phys. Soc.Jpn.,2007,75:053702.
[164] Fukui T, Fujiwara T, Hatsugai Y. Topological Meaning of Z2Numbers in Time Reversal Invari-ant Systems. J. Phys. Soc. Jpn.,2008,77:123705.
[165] Qi X L, Hughes T L, Zhang S C. Topological field theory of time-reversal invariant insulators.Phys. Rev. B,2008,78(19):195424.
[166] Wang Z, Qi X L, Zhang S C. Equivalent topological invariants of topological insulators. New J.Phys.,2010,12:065007.
[167] Liu C X, Qi X L, Zhang H, et al. Model Hamiltonian for topological insulators. Phys. Rev. B,2010,82(4):045122.
[168] Maiani L, Petronzio R, Zavattini E. Efects of nearly massless, spin-zero particles on lightporpagation in a magnetic field. Phys. Lett. B,1986,175:359.
[169] Mills D L, Burstein E. Polaritons: the electromagnetic modes of media. Rep. Prog. Phys.,1974,37:817.
[170] Rafelt G, Stodolsky L. Mixing of the photon with low-mass particles. Phys. Rev. D,1988,37:1237.
[171] Cameron R, Cantatore G, Melissinos A C, et al. Search for nearly massless, weakly coupledparticles by optical techniques. Phys. Rev. D,1993,47:3707.
[172] Lohndorf M, Moreland J, Kabos P, et al. Microcantilever torque magnetometry of thin magneticfilms. J. Appl. Phys.,2000,87:5995.
[173] Mamin H J, Budakian R, Chui B W, et al. Detection and manipulation polarization in small spinensembles. Phys. Rev. Lett.,2003,91:207604.
[174] Budakian R, Mamin H J, Chui B W, et al. Creating order from random fluctuations in small spinensembles. Science,2005,307:408.
[175] Raghu S, Qi X L, Honerkamp C, et al. Topological Mott Insulators. Phys. Rev. Lett.,2008,100(15):156401.
[176] Shitade A, Katsura H, KunesˇJ, et al. Quantum Spin Hall Efect in a Transition Metal OxideNa2IrO3. Phys. Rev. Lett.,2009,102(25):256403.
[177] Guo H M, Franz M. Three-Dimensional Topological Insulators on the Pyrochlore Lattice. Phys.Rev. Lett.,2009,103(20):206805.
[178] Pesin D, Balents L. Mott physics and band topology in materials with strong spin-orbit interac-tion. Nat. Phys.,2010,6:376.
[179] Prewitt C T, Shannon R D, Rogers D B, et al. The C rare earth oxide-corundum transition andcrystal chemistry of oxides having the corundum structure. Inorg. Chem.,1969,8:1985.
[180] Nebenzahl I, Weger M. Band structure of the3d-t2gsub-shell of V2O3and Ti2O3in the tight-binding approximation. Phil. Mag.,1971,24:1119.
[181] Harrison W A. Elementary Electronic Structure. Singapore: World Scientific,1999:67–87.
[182] Kim B J, Jin H, Moon S J, et al. Novel Jef=1/2Mott State Induced by Relativistic Spin-OrbitCoupling in Sr2IrO4. Phys. Rev. Lett.,2008,101(7):076402.
[183] Kim B J, Ohsumi H, Komesu T, et al. Phase-Sensitive Observation of a Spin-Orbital Mott Statein Sr2IrO4. Science,2009,323(5919):1329–1332.
[184] Brunel M, Bergevin F D. Difrraction of X-rays by Magnetic Materials. II. Measurements onAntiferromagnetic Fe2O3. Acta. Cryst.,1987, A37:324.
[185] Morrish A H. Canted Antiferromagnetism: Hermatite. Singapore: World Scientific,1994:57–100.
[186] Catti M, Valerio G, Dovesi R. Theoretical study of electronic, magnetic, and structural propertiesof α-Fe2O3(hematite). Phys. Rev. B,1995,51(12):7441–7450.
[187] Qi X L, Li R, Zang J, et al. Inducing a Magnetic Monopole with Topological Surface States.Science,2009,323(5918):1184–1187.
[188] Fu L, Kane C L. Superconducting Proximity Efect and Majorana Fermions at the Surface of aTopological Insulator. Phys. Rev. Lett.,2008,100(9):096407.
[189] Qi X L, Hughes T L, Raghu S, et al. Time-Reversal-Invariant Topological Superconductors andSuperfluids in Two and Three Dimensions. Phys. Rev. Lett.,2009,102(18):187001.
[190] Kuroda K, Arita M, Miyamoto K, et al. Hexagonally Deformed Fermi Surface of the3D Topo-logical Insulator Bi2Se3. Phys. Rev. Lett.,2010,105(7):076802.
[191] Zhang Y, He K, Chang C Z, et al. Crossover of the three-dimensional topological insulatorBi2Se3to the two-dimensional limit. Nat. Phys.,2010,6:584–588.
[192] Cheng P, Song C, Zhang T, et al. Landau Quantization of Topological Surface States in Bi2Se3.Phys. Rev. Lett.,2010,105(7):076801.
[193] Hanaguri T, Igarashi K, Kawamura M, et al. Momentum-resolved Landau-level spectroscopy ofDirac surface state in Bi2Se3. Phys. Rev. B,2010,82(8):081305.
[194] Wang J, Li W, Deng P, et al. Power laws and STM image of standing wave of the topologicalsurface states. Submitted to Phys. Rev. Lett., preprint at arXiv: cond-mat/1105.1957.
[195] Lu H Z, Shan W Y, Yao W, et al. Massive Dirac fermions and spin physics in an ultrathin filmof topological insulator. Phys. Rev. B,2010,81(11):115407.
[196] Roth L M, Zeiger H J, Kaplan T A. Generalization of the Ruderman-Kittel-Kasuya-YosidaInteraction for Nonspherical Fermi Surfaces. Phys. Rev.,1966,149(2):519–525.
[197] Crommie M F, Lutz C P, Eigler D M. Imaging standing waves in a two-dimensional electrongas. Nature,1993,363:524–527.
[198] Lee W C, Wu C, Arovas D P, et al. Quasiparticle interference on the surface of the topologicalinsulator Bi2Te3. Phys. Rev. B,2009,80(24):245439.
[199] Zhou X, Fang C, Tsai W F, et al. Theory of quasiparticle scattering in a two-dimensional systemof helical Dirac fermions: Surface band structure of a three-dimensional topological insulator.Phys. Rev. B,2009,80(24):245317.
[200] Wang Q H, Wang D, Zhang F C. Electronic structure near an impurity and terrace on the surfaceof a three-dimensional topological insulator. Phys. Rev. B,2010,81(3):035104.
[201] Okada Y, Dhital C, Zhou W, et al. Direct Observation of Broken Time-Reversal Symmetry on theSurface of a Magnetically Doped Topological Insulator. Phys. Rev. Lett.,2011,106(20):206805.
[202] Linder J, Tanaka Y, Yokoyama T, et al. Unconventional Superconductivity on a TopologicalInsulator. Phys. Rev. Lett.,2010,104(6):067001.
[203] Seradjeh B, Moore J E, Franz M. Exciton Condensation and Charge Fractionalization in aTopological Insulator Film. Phys. Rev. Lett.,2009,103(6):066402.
[204] Chen Y L, Chu J H, Analytis J G, et al. Massive Dirac Fermion on the Surface of a MagneticallyDoped Topological Insulator. Science,2010,329(5992):659–662.
[205] Li Y Y, Wang G, Zhu X G, et al. Intrinsic Topological Insulator Bi2Te3Thin Films on Si andTheir Thickness Limit. Advanced Materials,2010,22(36):4002–4007.
[206] Ren Z, Taskin A A, Sasaki S, et al. Large bulk resistivity and surface quantum oscillations inthe topological insulator Bi2Te2Se. Phys. Rev. B,2010,82(24):241306.
[207] Liu M, Chang C Z, Zhang Z, et al. Electron interaction-driven insulating ground state in Bi2Se3topological insulators in the two-dimensional limit. Phys. Rev. B,2011,83(16):165440.