基于拓扑绝缘体表面准一维体系电子结构及输运性质研究
|
摘要
拓扑绝缘体是一种完全不同于传统金属与绝缘体的新型量子物态,其体电子态是有能隙的绝缘体,而表面/边缘是无能隙的金属态,而且这种无能隙的表面/边缘态受到时间反演对称性的保护.这完全是由材料本身的自旋-轨道耦合作用导致能带反转引起的.拓扑绝缘体的独特性质使其迅速成为近年来凝聚态物理研究领域的一个热点.本论文在弹道输运理论框架下,采用传输矩阵方法以及Landaur-Biittiker公式,研究拓扑绝缘体表面上金属门电极及铁磁近邻作用限制形成的几种准一维体系的电子结构和输运性质及其外场调控问题,旨在为未来基于拓扑绝缘体表面态的纳米(自旋)电子器件的设计提供理论基础.
全文共分为六章.第一章为绪论,简要介绍了量子自旋霍尔效应和拓扑绝缘体的基本概论,以及几种典型基于拓扑绝缘体表面态低维体系的实验实现与制备.第二章中,我们较详细介绍了介观量子输运中常用的理论研究方法,即矩阵方法和非平衡格林函数方法.
第三章研究了三维拓扑绝缘体薄膜表面态在金属门电极方势阱的限制下一维波导体系.从表面态有效哈密顿量出发,通过求解对应的本征方程获得了电子结构,包括能带结构和自旋极化分布.结果表明：在势阱中存在表面束缚态,其实空间中电子密度分布局域在势阱内,而在势阱外是指数衰减的；束缚态子能级与波矢成准线性的色散关系；当波矢b>0时,通道内电子主要占据薄膜的上表面,而ky<0时,电子主要占据薄膜的下表面；由于上下表面的耦合作用,具有相同电子密度分布的上表面和下表面束缚态的自旋极化方向是相反的.
第四章研究了电势阱对三维拓扑绝缘体表面态朗道能级的影响.通过数值计算方法求解体系相应的Dirac方程,获得了一些有趣的结果：在一定的范围内,能量既是垂直磁场的函数又是波矢的函数,而且导带和价带不再关于最低朗道能级对称；当电子的回旋轨道中心位于势阱内时,局域态密度中的价带部分将被抑制；当回旋轨道中心不太靠近势阱的两个边界,能级趋于平坦,与波矢无关.有趣的是,我们发现这种限制势不但改变朗道能级而且产生了沿着势阱的边界传播的边界态,导带上边界态的几率密度和自旋极化主要分布在势阱内而在势阱外是衰减的,但是价带上边界态的几率密度和自旋极化主要分布在势阱外而在势阱内是衰减的.
第五章从硅烯有效Dirac哈密顿量出发,研究了不均匀局域电场和铁磁近邻交换场形成的准一维通道内的自旋和谷过滤效应.利用传输矩阵方法和Landaur-Buttiker公式,我们得到的结果表明：两界面之间的全内反射使得通道内存在束缚态,且电场和交换场对具有不同自旋和谷指标的导带和价带产生不同的效应；发现可以存在沿通道自旋和谷极化的输运电流,它的极化程度受局域电场和交换场的调制,并得到了在这种电磁波导结构中实现完全自旋极化和谷极化电流的条件.我们的结果为实验上实现有效操控硅烯中电子自旋和谷自由度提供了一种方案.
第六章中,我们对本文的工作进行了总结和归纳,并对基于拓扑绝缘体表面态准一维体系的研究以及在纳米(自旋)电子器件中的应用进行了展望.
The topological insulator (TI), a new phase of quantum matter, is very dif-ferent from the traditional metal and insulator. These materials are electrically insulating in the bulk but have current-carrying gapless Dirac surface/edge states, whose gaplessness is protected by time-reversal symmetry. This occurs as a result of the electron spin-orbit coupling (SOC) which leads to the band-invert for the materials. Due to the unique properties, the TI has been a hot topic in condensed matter physics community in recent years. In this thesis, the electronic structure and spin-related properties of the surface states of topological insulators, which modulated by electric field and ferromagnetic exchange field, have been theoreti-cally investigated by the transfer matrix method. The purpose of this study is for providing physical basis for the design of nano-electronical devices and low-energy consumption spintronics devices in the future.
The thesis is divided into six chapters. In the first chapter, we briefly introduce Quantum Spin Hall Effect and TIs, as well as the fabrication techniques of quasi-one-dimensional (QlD) system of TIs. In the second chapter, we provide a detailed introduction to the transfer matrix and non-equilibrium Green function method which are often used in the study of mesoscopic quantum transport.
In the third chapter, based on the Dirac equation we study the electronic structure and spin polarization of the surface states of a three-dimensional topo-logical insulator (3D TI) thin film modulated by an electrical potential well. It is demonstrated that, there exist confined surface states in the potential well, in which the electron density is almost localized inside the well and exponentially decays outside in real space. The subbands of confined states are quasilinear with respect to the propagating wavevector. Importantly, a large proportion of electrons with ky>0occupy the top surface of the thin film, while for ky<0, most elec-trons occupy the bottom surface of the film in the Q1D quantum well region; The top and bottom surface confined states with the same density distribution have opposite spin polarizations due to the hybridization between the two surfaces.
In the fourth chapter, by using a numerical method, we study the effect of an electric square-well potential on the Landau level (LL) spectrum for surface states of a3D TI. The results show that the energy spectrum as a function of both the magnetic field and the wavevector in certain range. It is demonstrated that the conduction and valence bands are no longer symmetric with respect to the lowest subband, and the valence branch is suppressed when the center of electron cyclotron orbit is inside the well. However, the energy bands trend to flat when the cyclotron orbit center is not too close to the well boundaries (corners). Interestingly, we find that the confining potential not only shifts LLs but also creates propagating interface states near boundaries. Moreover, the probability densities and spin polarization distributions of interface states in conduction band oscillate mainly inside the well and decay outside, while those in valence band oscillate outside and decay inside the well.
In the fifth chapter, by using the transfer matrix method and Landaur-Buttiker formula, we theoretically study the spin and valley transport properties of Dirac electrons in a channel created by the local exchange field and local per-pendicular electric field on silicene sheet. The multiple total internal reflections at the interfaces result in the bound states in the channel, which behaves like an electronic waveguide. The different effects of local electric and exchange fields on both conduction and valence bands for bound states are identified by spin and valley indices. Interestingly, the electron transmitting along the channel can be both spin-and valley-polarized, and its degree of polarization can be tuned by electric and/or exchange fields. And, in particular, the condition for fully spin-and valley-polarization is obtained. Our findings may provide a scheme for efec-tively manipulating spin and valley degrees of freedom in this magnetic waveguide structure on a silicene sheet.
In chapter six, a summary of the work and a outlook of the transport prop-erties of quasi-1D TI under the electric field and ferromagnetic modulation are given.
全文共分为六章.第一章为绪论,简要介绍了量子自旋霍尔效应和拓扑绝缘体的基本概论,以及几种典型基于拓扑绝缘体表面态低维体系的实验实现与制备.第二章中,我们较详细介绍了介观量子输运中常用的理论研究方法,即矩阵方法和非平衡格林函数方法.
第三章研究了三维拓扑绝缘体薄膜表面态在金属门电极方势阱的限制下一维波导体系.从表面态有效哈密顿量出发,通过求解对应的本征方程获得了电子结构,包括能带结构和自旋极化分布.结果表明：在势阱中存在表面束缚态,其实空间中电子密度分布局域在势阱内,而在势阱外是指数衰减的；束缚态子能级与波矢成准线性的色散关系；当波矢b>0时,通道内电子主要占据薄膜的上表面,而ky<0时,电子主要占据薄膜的下表面；由于上下表面的耦合作用,具有相同电子密度分布的上表面和下表面束缚态的自旋极化方向是相反的.
第四章研究了电势阱对三维拓扑绝缘体表面态朗道能级的影响.通过数值计算方法求解体系相应的Dirac方程,获得了一些有趣的结果：在一定的范围内,能量既是垂直磁场的函数又是波矢的函数,而且导带和价带不再关于最低朗道能级对称；当电子的回旋轨道中心位于势阱内时,局域态密度中的价带部分将被抑制；当回旋轨道中心不太靠近势阱的两个边界,能级趋于平坦,与波矢无关.有趣的是,我们发现这种限制势不但改变朗道能级而且产生了沿着势阱的边界传播的边界态,导带上边界态的几率密度和自旋极化主要分布在势阱内而在势阱外是衰减的,但是价带上边界态的几率密度和自旋极化主要分布在势阱外而在势阱内是衰减的.
第五章从硅烯有效Dirac哈密顿量出发,研究了不均匀局域电场和铁磁近邻交换场形成的准一维通道内的自旋和谷过滤效应.利用传输矩阵方法和Landaur-Buttiker公式,我们得到的结果表明：两界面之间的全内反射使得通道内存在束缚态,且电场和交换场对具有不同自旋和谷指标的导带和价带产生不同的效应；发现可以存在沿通道自旋和谷极化的输运电流,它的极化程度受局域电场和交换场的调制,并得到了在这种电磁波导结构中实现完全自旋极化和谷极化电流的条件.我们的结果为实验上实现有效操控硅烯中电子自旋和谷自由度提供了一种方案.
第六章中,我们对本文的工作进行了总结和归纳,并对基于拓扑绝缘体表面态准一维体系的研究以及在纳米(自旋)电子器件中的应用进行了展望.
The topological insulator (TI), a new phase of quantum matter, is very dif-ferent from the traditional metal and insulator. These materials are electrically insulating in the bulk but have current-carrying gapless Dirac surface/edge states, whose gaplessness is protected by time-reversal symmetry. This occurs as a result of the electron spin-orbit coupling (SOC) which leads to the band-invert for the materials. Due to the unique properties, the TI has been a hot topic in condensed matter physics community in recent years. In this thesis, the electronic structure and spin-related properties of the surface states of topological insulators, which modulated by electric field and ferromagnetic exchange field, have been theoreti-cally investigated by the transfer matrix method. The purpose of this study is for providing physical basis for the design of nano-electronical devices and low-energy consumption spintronics devices in the future.
The thesis is divided into six chapters. In the first chapter, we briefly introduce Quantum Spin Hall Effect and TIs, as well as the fabrication techniques of quasi-one-dimensional (QlD) system of TIs. In the second chapter, we provide a detailed introduction to the transfer matrix and non-equilibrium Green function method which are often used in the study of mesoscopic quantum transport.
In the third chapter, based on the Dirac equation we study the electronic structure and spin polarization of the surface states of a three-dimensional topo-logical insulator (3D TI) thin film modulated by an electrical potential well. It is demonstrated that, there exist confined surface states in the potential well, in which the electron density is almost localized inside the well and exponentially decays outside in real space. The subbands of confined states are quasilinear with respect to the propagating wavevector. Importantly, a large proportion of electrons with ky>0occupy the top surface of the thin film, while for ky<0, most elec-trons occupy the bottom surface of the film in the Q1D quantum well region; The top and bottom surface confined states with the same density distribution have opposite spin polarizations due to the hybridization between the two surfaces.
In the fourth chapter, by using a numerical method, we study the effect of an electric square-well potential on the Landau level (LL) spectrum for surface states of a3D TI. The results show that the energy spectrum as a function of both the magnetic field and the wavevector in certain range. It is demonstrated that the conduction and valence bands are no longer symmetric with respect to the lowest subband, and the valence branch is suppressed when the center of electron cyclotron orbit is inside the well. However, the energy bands trend to flat when the cyclotron orbit center is not too close to the well boundaries (corners). Interestingly, we find that the confining potential not only shifts LLs but also creates propagating interface states near boundaries. Moreover, the probability densities and spin polarization distributions of interface states in conduction band oscillate mainly inside the well and decay outside, while those in valence band oscillate outside and decay inside the well.
In the fifth chapter, by using the transfer matrix method and Landaur-Buttiker formula, we theoretically study the spin and valley transport properties of Dirac electrons in a channel created by the local exchange field and local per-pendicular electric field on silicene sheet. The multiple total internal reflections at the interfaces result in the bound states in the channel, which behaves like an electronic waveguide. The different effects of local electric and exchange fields on both conduction and valence bands for bound states are identified by spin and valley indices. Interestingly, the electron transmitting along the channel can be both spin-and valley-polarized, and its degree of polarization can be tuned by electric and/or exchange fields. And, in particular, the condition for fully spin-and valley-polarization is obtained. Our findings may provide a scheme for efec-tively manipulating spin and valley degrees of freedom in this magnetic waveguide structure on a silicene sheet.
In chapter six, a summary of the work and a outlook of the transport prop-erties of quasi-1D TI under the electric field and ferromagnetic modulation are given.
引文
[1]M. N. Baibich, J. M. Broto, A. Fert, F. Nguyen Van Dau, and F. Petroff. Giant Magnetoresistance of (001)Fe/(001)Cr Magnetic Superlattices. Phys. Rev. Lett., 1988,61:2472.
[2]S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, D. M. Treger. Spintronics:A Spin-Based Electronics Vision for the Future. Science,2001,294:1488.
[3]Igor. Zutic, Jaroslav. Fabian and S. Das Sarma. Spintronics:Fundamentals and applications. Rev. Mod. Phys.,2004,76:323.
[4]J. E. Hirsch. Spin Hall Effect. Phys. Rev. Lett.,1999,83:1834.
[5]Shuichi Murakami, Naoto Nagaosa, Shou-Cheng Zhang. Dissipationless Quantum Spin Current at Room Temperature. Science,2003,301:1348; Jairo Sinova, Dimitrie Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, and A. H. MacDonald. Universal Intrinsic Spin Hall Effect. Phys. Rev. Lett.,2004,92:126603.
[6]Y. K. Kato, R. C. Myers, A. C. Gossard, D. D. Awschalom. Observation of the Spin Hall Effect in Semiconductors. Science,2004,306:1910; J. Wunderlich, B. Kaestner, J. Sinova, and T. Jungwirth. Experimental Observation of the Spin-Hall Effect in a Two-Dimensional Spin-Orbit Coupled Semiconductor System. Phys. Rev. Lett.,2004,94:047204.
[7]W. Kohn. Theory of the insulating state. Phys. Rev.,1964,133:A171.
[8]K. v. Klitzing, G. Dorda and M. Pepper. New Method for High-Accuracy De-termination of the Fine-Structure Constant Based on Quantized Hall Resistance. Phys. Rev. Lett.,1980,45:494.
[9]J. E. Avron, D. Osadchy, R. Seiler. A topological look at the Quantum Hall Effect. Phys. Today,2003,56:38.
[10]C. L. Kane and E. J. Mele. Quantum Spin Hall Effect in Graphene. Phys. Rev. Lett..2005,95:226801.
[11]B. Andrei Bernevig, Taylor L. Hughes, Shou-Cheng Zhang. Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells. Science,2006, 314:1757.
[12]Markus Konig, Steffen Wiedmann, Christoph Bruene, Andreas Roth, Hartmut Buhmann, Laurens W. Molenkamp, Xiao-Liang Qi, Shou-Cheng Zhang. Quantum Spin Hall insulator state in HgTe Quantum Wells. Science,2007,318:766.
[13]Shuichi Murakami. Quantum Spin Hall Effect and Enhanced Magnetic Response by Spin-Orbit Coupling. Phys. Rev. Lett.,2007,97:236805.
[14]Chaoxing Liu, Taylor L. Hughes, Xiao-Liang Qi, KangWang, and Shou-Cheng Zhang. Quantum Spin Hall Effect in Type-Ⅱ Semiconductors. Phys. Rev. Lett. 2008,100:236601.
[15]Atsuo Shitade, Hosho Katsura, Jan Kun, Xiao-Liang Qi, Shou-Cheng Zhang, and Naoto Nagaosa. Quantum Spin Hall Effect in a Transition Metal Oxide Na2-IrO3. Phys. Rev. Lett.,2009,102:256403.
[16]Ivan Knez and R. R. Du. Finite conductivity in mesoscopic Hall bars of inverted InAs/GaSb quantum wells. Phys. Rev. B,2010,81:201301.
[17]Xiao-Liang Qi and Shou-Cheng Zhang. The quantum spin Hall effect and topo-logical insulators. Phys. Today,2010,63:33.
[18]C. L. Kane and E. J. Mele. Z2 Topological Order and the Quantum Spin Hall Effect. Phys. Rev. Lett.,2005,95:146802.
[19]Charles L. Kane and Eugene J. Mele. A New Spin on the Insulating State. Science, 2006,314:1692.
[20]J. Barnas, A. Fuss, R. E. Camley, P. Griinberg, and W. Zinn. Novel magnetoresis-tance effect in layered magnetic structures:Theory and experiment. Phys. Rev. B,1990,42:8110; Gary A. Prinz. Magnetoelectronics. Science,1998,282:1660.
[21]S. S. P. Parkin, D. Mauri. Spin engineering:Direct determination of the Ruderman-Kittel-Kasuya-Yosida far-field range function in ruthenium. Phys. Rev. B,1991,44:7131.
[22]J. S. Moodera, Lisa R. Kinder, Terrilyn M. Wong, and R. Meservey. Large Magne-toresistance at Room Temperature in Ferromagnetic Thin Film Tunnel Junctions. Phys. Rev. Lett.,1994,74:3273.
[23]G. H. Koha, H. J. Kim, W. C. Jeong, J. H. Oh, J. H. Park, S. Y. Lee, G. T. Jeong, I. J. Hwang, T. W. Kim, J. E. Lee, S. O. Park, U. I. Jeong, H. S. Jeong, Kinam Kim. Fabrication of high performance 64 kb MRAM. J. of Magnetism and Magnetic Materials,2004,272:1941.
[24]S. Das Sarma, Jaroslav Fabian, Xuedong Hu, Igor Zutic. Spin electronics and spin computation. Solid State communications,2001,119:207.
[25]Supriyo Datta and Biswajit Das. Electronic analog of the elecro-optic modulator. Appl. Phys. Lett.,1990,56:665.
[26]H. Ohno. Making Nonmagnetic Semiconductor Ferromagnetic. Science,1998, 281:951.
[27]Jun-ichiro Inoue, Gerrit E. W. Bauer, Laurens W. Molenkamp. Suppression of the persistent spin Hall current by defect scattering. Phys. Rev. B,2004,70: 041303(R).
[28]L. Sheng, D. N. Sheng, and C. S. Ting. Spin-Hall Effect in Two-Dimensional Electron Systems with Rashba Spin-Orbit Coupling and Disorder. Phys. Rev. Lett.,2005,94:016602; D. N. Sheng, L. Sheng, Z. Y. Weng, and F. D. M. Haldane. Spin Hall effect and spin transfer in a disordered Rashba model. Phys. Rev. B,2005,72:153307.
[29]Xing-Tao An, Yan-Yang Zhang, Jian-Jun Liu, and Shu-Shen Li. Quantum spin Hall effect induced by electric field in silicene. Appl. Phys. Lett.,2013,102: 043113.
[30]A. H. Castro Neto, N. M. R. Peres, K. S. Novoselov and A. K. Geim. The electronic properties of graphene. Rev. Mod. Phys.,2009,81:109.
[31]P. R. Wallace. The Band Theory of Graphite. Phys. Rev.,1947,71:622.
[32]J. C. Slonczewski, P. R. Weiss. Band Structure of Graphite. Phys. Rev.,1958, 109:272.
[33]J. W. McClure. Analysis of Multicarrier Galvanomagnetic Data for Graphite. Phys. Rev.,1958,112:715.
[34]J. Gonzalez, F. Guinea, and M. A. H. Vozmediano. Unconventional Quasiparticle Lifetime in Graphite. Phys. Rev. Lett.,1996,77:3589.
[35]F. D. M. Haldane. Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly". Phys. Rev. Lett.,1988, 61:2015.
[36]K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov. Electric Field Effect in Atomically Thin Carbon Films. Science,2004,306:666; K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos and A. A. Firsov. Two-dimensional gas of massless Dirac fermions in graphene. Nature,2005,438: 197.
[37]Daniel Huertas-Hernando, F. Guinea, and Arne Brataas. Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps. Phys. Rev. B,2006, 74:155426.
[38]Hongki Min, J. E. Hill, N. A. Sinitsyn. B. R. Sahu, Leonard Kleinman, and A. H. MacDonald. Intrinsic and Rashba spin-orbit interactions in graphene sheets. Phys. Rev. B,2006,74:165310.
[39]J. C. Boettger, S. B. Trickey. First-principles calculation of the spin-orbit splitting in graphene. Phys. Rev. B,2007,75:121402.
[40]Yugui Yao, Fei Ye, Xiao-Liang Qi, Shou-Cheng Zhang, and Zhong Fang. Spin-orbit gap of graphene:First-principles calculations. Phys. Rev. B,2007,75:041401.
[41]M. Gmitra, S. Konschuh, C. Ertler, C. Ambrosch-Draxl, and J. Fabian. Band-structure topologies of graphene:Spin-orbit coupling effects from first principles. Phys. Rev. B,2009,80:235431.
[42]Liang Fu, C. L. Kane and E. J. Mele. Topological insulator in Three Dimensions. Phys. Rev. Lett.,2007,98:106803.
[43]J. E. Moore and L. Balents. Topological invariants of time-reversal-invariant band structures. Phys. Rev. B,2007,75:121306(R).
[44]Rahul Roy. Z2 classification of quantum spin Hall systems:An approach using time-reversal invariance. Phys. Rev. B,2009,79:195321.
[45]Liang Fu and C. L. Kane. Topological insulators with inversion symmetry. Phys. Rev. B,2007,76:045302.
[46]D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava and M. Z. Hasan. A topological Dirac insulator in a quantum spin Hall phase. Nature,2008,452: 970.
[47]F. Patthey, W.-D. Schneider, H. Micklitz. Photoemission study of the Bi(111) surface. Phys. Rev. B,1994,49:11293.
[48]S Agergaard, Ch Sodergaard, H Li, M B Nielsen, S V Hoffmann, Z Li and Ph Hofmann. The effect of reduced dimensionality on a semimetal: the electronic structure of the Bi(110) surface. New J. Phys.,2001,3:15.
[49]Christian R. Ast and Hartmut Hochst. Fermi Surface of Bi(111) Measured by Photoemission Spectroscopy. Phys. Rev. Lett.,2001,87:177602.
[50]Ph. Hofmann. The surfaces of bismuth:Structural and electronic properties. Prog. Surf. Sci.,2006,81:191.
[51]T. Hirahara, T. Nagao, I. Matsuda, G. Bihlmayer, E. V. Chulkov, Yu. M. Koroteev, P. M. Echenique, M. Saito, and S. Hasegawa. Role of Spin-Orbit Coupling and Hybridization Effects in the Electronic Structure of Ultrathin Bi Films. Phys. Rev. Lett.,2006,97:146803.
[52]Haijun Zhang, Chao-Xing Liu, Xiao-Liang Qi, Xi Dai, Zhong Fang and Shou-Cheng Zhang. Topological insulators in Bi2Se3,Bi2Te3 and Sb2Te.3 with a single Dirac cone on the surface. Nat. Phys.,2009,5:438.
[53]Y. Xia, D. Qian, D. Hsieh, L.Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava and M. Z. Hasan. Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Nat. Phys.,2009,5:398.
[54]Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, Z.-X. Shen. Experimental Realization of a Three-Dimensional Topological Insulator, Bi2Te3. Science,2009,325:178.
55] Chao-Xing Liu, Xiao-Liang Qi, HaiJun Zhang, Xi Dai, Zhong Fang, and Shou-Cheng Zhang. Model Hamiltonian for topological insulators. Phys. Rev. B,2010, 82:045122.
[56]D. Hsieh, Y. Xia, D. Qian, L. Wray, J. H. Dil, F. Meier, J. Osterwalder. L. Patthey, J. G. Checkelsky, N. P. Ong, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer. Y. S. Hor, R. J. Cava and M. Z. Hasan. A tunable topological insulator in the spin helical Dirac transport regime. Nautre,2009,460:1101.
[57]Pedram Roushan, Jungpil Seo, Colin V. Parker, Y. S. Hor, D. Hsieh, Dong Qian, Anthony Richardella, M. Z. Hasan, R. J. Cava and Ali Yazdani. Topological surface states protected from backscattering by chiral spin texture. Nautre(London), 2009,460:1106; Tong Zhang, Peng Cheng, Xi Chen, Jin-Feng Jia, Xucun Ma, Ke He, Lili Wang, Haijun Zhang, Xi Dai, Zhong Fang, Xincheng Xie, and Qi-Kun Xue. Experimental Demonstration of Topological Surface States Protected by Time-Reversal Symmetry. Phys. Rev. Lett.,2009,103:266803.
[58]J. Linder, T. Yokoyama,and A. Sudbo. Anomalous finite size effects on surface states in the topological insulator Bi2Se3. Phys. Rev. B,2009,80:205401.
[59]Chao-Xing Liu, HaiJun Zhang, Binghai Yan, Xiao-Liang Qi, Thomas Frauen-heim, Xi Dai, Zhong Fang and Shou-Cheng Zhang. Oscillatory crossover from two-dimensional to three-dimensional topological insulators. Phys. Rev. B,2010, 81:041307.
[60]Hai-Zhou Lu, Wen-Yu Shan, Wang Yao, Qian Niu, and Shun-Qing Shen. Massive Dirac fermions and spin physics in an ultrathin film of topological insulator. Phys. Rev. B,2010,81:115407.
[61]Wen-Yu Shan, Hai-Zhou Lu and Shun-Qing Shen. Effective continuous model for surface states and thin films of three-dimensional topological insulators. New J. Phys.,2010,12:043048.
[62]Yao-Yi Li, Guang Wang, Xie-Gang Zhu, Min-Hao Liu, Cun Ye, Xi Chen, Ya-Yu Wang, Ke He, Li-Li Wang, Xu-Cun Ma, Hai-Jun Zhang, Xi Dai, Zhong Fang, Xin-Cheng Xie, Ying Liu, Xiao-Liang Qi, Jin-Feng Jia, Shou-Cheng Zhang, and Qi-Kun Xue. Intrinsic topological insulator Bi2Te-3 thin films on Si and their thickness limit. Adv. Mater.,2010,22:4002.
[63]Guanhua Zhang, Huajun Qin, Jing Teng, Jiandong Guo, Qinlin Guo, Xi Dal, Zhong Fang, and Kehui Wu. Quintuple-layer epitaxy of thin films of topological insulator Bi2Se3. Appl. Phys. Lett.,2009,95:053114.
[64]Yusuke Sakamoto, Toru Hirahara, Hidetoshi Miyazaki, Shin-ichi Kimura, and Shuji Hasegawa. Spectroscopic evidence of a topological quantum phase transi-tion in ultrathin Bi2Se3 films. Phys. Rev. B,2010,81:165432.
[65]Yi Zhang, Ke He, Cui-Zu Chang, Can-Li Song, Li-Li Wang, Xi Chen, Jin-Feng Jia, Zhong Fang, Xi Dai, Wen-Yu Shan, Shun-Qing Shen, Qian Niu, Xiao-Liang Qi, Shou-Cheng Zhang, Xu-Cun Ma and Qi-Kun Xue. Crossover of the three-dimensional topological insulator Bi2Se3 to the two-dimensional limit. Nat. Phys.,2010,6:584.
[66]Toru Hirahara, Yusuke Sakamoto, Yasuo Takeichi, Hidetoshi Miyazaki, Shin-ichi Kimura, Iwao Matsuda, Akito Kakizaki, and Shuji Hasegawa. Anomalous trans-port in an n-type topological insulator ultrathin Bi2Se3 film. Phys. Rev. B,2010, 82:155309.
[67]Minhao Liu, Cui-Zu Chang, Zuocheng Zhang, Yi Zhang, Wei Ruan, Ke He, Li-li Wang, Xi Chen, Jin-Feng Jia, Shou-Cheng Zhang, Qi-Kun Xue, Xucun Ma, and Yayu Wang. Electron interaction-driven insulating ground state in Bi2Se3 topological insulators in the two-dimensional limit. Phys. Rev. B,2011,83: 165440.
[68]Jian Wang, Ashley M. DaSilva, Cui-Zu Chang, Ke He, J. K. Jain, Nitin Samarth, Xu-Cun Ma, Qi-Kun Xue, and Moses H. W. Chan. Evidence for electron-electron interaction in topologicalinsulator thin films. Phys. Rev. B,2011,83:245438.
[69]Boubekeur Lalmi, Hamid Oughaddou, Hanna Enriquez, Abdelkader Kara, Sebastien Vizzini, Benidicte Ealet, and Bernard Aufray. Epitaxial growth of a silicene sheet. Appl. Phys. Lett.,2010,97:223109.
[70]Rong Yang, Lianchang Zhang, Yi Wang, Zhiwen Shi, Dongxia Shi, Hongjun Gao, Enge Wang, and Guangyu Zhang. An Anisotropic Etching Effect in the Graphene Basal Plane. Adv. Mater.,2010,22:4014.
[71]Lei Liu, Yingli Zhang, Wenlong Wang, Changzhi Gu, Xuedong Bai, and Enge Wang. Nanosphere Lithography for the Fabrication of Ultranarrow Graphene Nanoribbons and On-Chip Bandgap Tuning of Graphene. Adv. Mater.,2011, 23:1246.
[72]Zhiwen Shi, Rong Yang, Lianchang Zhang, Yi Wang, Donghua Liu, Dongxia Shi, Enge Wang, and Guangyu Zhang. Patterning Graphene with Zigzag Edges by Self-Aligned Anisotropic Etching. Adv. Mater.,2011,23:3061.
[73]Jin Seok Lee, Sarah Brittman, Dong Yu, and Hongkun Park. Vapor-Liquid-Solid and Vapor-Solid Growth of Phase-Change Sb2Te3 Nanowires and Sb2Te3/GeTe Nanowire Heterostructures. J. Am. Chem. Soc.,2008,130:6252.
[74]Yuri M. Zuev, Jin Seok Lee, Clement Galloy, Hongkun Park, and Philip Kim. Di-ameter Dependence of the Transport Properties of Antimony Telluride Nanowires. Nano Lett.,2010,10,3037.
[75]Desheng Kong, Jason C. Randel, Hailin Peng, Judy J. Cha, Stefan Meister, Keji Lai, Yulin Chen, Zhi-Xun Shen, Hari C. Manoharan, and Yi Cui. Topological Insulator Nanowires and Nanoribbons. Nano Lett.,2010,10,329.
[76]Hailin Peng, Keji Lai, Desheng Kong, Stefan Meister, Yulin Chen, Xiao-Liang Qi, Shou-Cheng Zhang, Zhi-Xun Shen and Yi Cui. Aharonov-Bohm interference in topological insulator nanoribbons. Nature Mater.,2010,9:225.
[77]Hanna Lind, Sven Lidin, and Ulrich Haussermann. Structure and bonding proper-ties of (Bi2Se3)m(Bi2)n stacks by first-principles density functional theory. Phys. Rev. B,2005,72:184101.
[78]Desheng Kong, Wenhui Dang, Judy J. Cha, Hui Li, Stefan Meister, Hailin Peng, Zhongfan Liu, and Yi Cui. Few-Layer Nanoplates of Bi2Se3 and Bi2Te3 with Highly Tunable Chemical Potential. Nano Lett.,2010,10,2245.
[79]Faxian Xiu, Liang He, Yong Wang, Lina Cheng, Li-Te Chang, Murong Lang, Guan Huang, Xufeng Kou, Yi Zhou, Xiaowei Jiang, Zhigang Chen, Jin Zou, Alexandros Shailos and Kang L. Wang. Manipulating surface states in topological insulator nanoribbons. Nature Nanotech.,2011,6:216.
[80]A. Scherer and H. G. Craighead. Fabrication of small laterally patterned multiple quantum wells. Appl. Phys. Lett.,1986,49:1284.
[81]M. Mehta, D. Reuter, A. Melnikov, and A. D. Wieck. Focused ion beam implan-tation induced site-selective growth of InAs quantum dots. Appl. Phys. Lett. 2007,91:123108.
[82]Nae-Man Park, Chel-Jong Choi, Tae-Yeon Seong, and Seong-Ju Park. Quantum Confinement in Amorphous Silicon Quantum Dots Embedded in Silicon Nitride. Phys. Rev. Lett.,2001,86:1355.
[83]S. Fafard, K. Hinzer, S. Raymond, M. Dion, J. McCaffrey, Y. Feng, S. Charbon-neau. Red-Emitting Semiconductor Quantum Dot Lasers. Science,1996,274: 1.350.
[84]Kai Chang and Wen-Kai Lou. Helical Quantum States in HgTe Quantum Dots with Inverted Band Structures. Phys. Rev. Lett.,2011,106:206802.
[85]Sungjae Cho, Dohun Kim, Paul Syers, Nicholas P. Butch, Johnpierre Paglione, and Michael S. Fuhrer. Topological Insulator Quantum Dot with Tunable Barriers. Nano Lett.,2011,12,469.
[86]Arijit Kundu, Alex Zazunov, Alfredo Levy Yeyati, Thierry Martin, and Reinhold Egger. Energy spectrum and broken spin-surface locking in topological insulator quantum dots. Phys. Rev. B,2011,83:125429.
[87]C. S. Tang and C. S. Chu. Coherent quantum transport in narrow constrictions in the presence of a finite-range longitudinally polarized time-dependent field. Phys. Rev. B,1999,60:1830.
[88]A. Reynoso, Gonzalo Usaj, M. J. Sanchez, and C. A. Balseiro. Theory of edge states in systems with Rashba spin-orbit coupling. Phys. Rev. B,2004,70: 235344.
[89]Zhigang Wang, Wei Zhang, and Ping Zhang. Magnetization in two-dimensional electron gas in a perpendicular magnetic field:The roles of edge states and spin-orbit coupling. Phys. Rev. B,2009,79:235327.
[90]J. Milton Pereira, Jr., V. Mlinar, and F. M. Peeters. Confined states and direction-dependent transmission in graphene quantum wells. Phys. Rev. B,2006,74: 045424.
[91]J. Milton Pereira, Jr., F. M. Peeters, and P. Vasilopoulos. Magnetic interface states in graphene-based quantum wires. Phys. Rev. B,2007,75:125433.
[92]Takehito Yokoyama, Alexander V. Balatsky, and Naoto Xagaosa. Gate-Controlled One-Dimensional Channel on the Surface of a 3D Topological Insulator. Phys. Rev. Lett.,2010,104:246806.
[93]Mark Johnson, Brian R. Bennett, M. J. Yang, M. M. Miller and B. V. Shanabrook. Hybrid Hall effect device. Appl. Phys. Lett.,1997,71:974; V. Kubrak, A. Neumann, B. L. Gallagher, P. C. Main, M. Henini, C. H. Marrows2 and B. J. Hickey. Magneto-resistance and Hall magnetometry of single submicron ferromag-netic structures. J. Appl. Phys.,2000,87:5986.
[94]H. A. Carmona, A. K. Geim, A. Nogaret, P. C. Main, T.J. Foster, and M. Henini, S.P. Beaumont, M. G. Blamire. Two Dimensional Electrons in a Lateral Magnetic Superlattice. Phys. Rev. Lett.,1995,74:3009; P. D. Ye, D. Weiss, R.R. Ger-hardts, M. Seeger, K. von Klitzing, K. Eberl, and H. Nickel. Electrons in a Periodic Magnetic Field Induced by a Regular Array of Micromagnets. Phys. Rev. Lett., 1995,74:3013.
[95]A. Nogaret, S. J. Bending, and M. Henini. Resistance Resonance Effects through Magnetic Edge States. Phys. Rev. Lett.,2000,84:2231.
[96]K. S. Novoselov, A. K. Geim, S. V. Dubonos, Y. G. Cornelissens, F. M. Peeters, and J. C. Maan. Scattering of ballistic electrons at a mesoscopic spot of strong magnetic field. Phys. Rev. B,2002,65:233312.
[97]M. Cerchez, S. Hugger, and T. Heinzel. Effect of edge transmission and elastic scattering on the resistance of magnetic barriers:Experiment and theory. Phys. Rev. B,2007,75:035341.
[98]T. Ando, T. Nakashini, and R. Saito. Berry's Phase and Absence of Back Scatter-ing in Carbon Nanotubes. J. Phys. Soc. Jpn.,1998,67:2857.
[99]Vadim V. Cheianov and Vladimir I. Fal'ko. Phys. Rev. B,2006,74:041403.
[100]M. I. Katsnelson, K. S. Novoselov, and A. K. Geim. Chiral tunnelling and the Klein paradox in graphene. Nat. Phys.,2006,2:620.
[101]A. De Martino, L. Dell'Anna, and R. Egger. Magnetic Confinement of Massless Dirac Fermions in Graphene. Phys. Rev. Lett.,2007,98:066802.
[102]Su-Yang Xu, Madhab Neupane, Chang Liu, Duming Zhang, Anthony Richardella, L. AndrewWray, Nasser Alidoust, Mats Leandersson, Thiagarajan Balasubrama-nian, Jaime Sanchez-Barriga, Oliver Rader, Gabriel Landolt. Bartosz Slomski, Jan Hugo Dil, Jurg Osterwalder, Tay-Rong Chang, Horng-Tay Jeng, Hsin Lin, Arun Bansil, Nitin Samarth and M. Zahid Hasan. Hedgehog spin texture and Berry's phase tuning in a magnetic topological insulator. Nat. Phys.,2012,8:616.
[103]A. Kandala, A. Richardella, D. W. Rench, D. M. Zhang, T. C. Flanagan, and N. Samarthb. Growth and characterization of hybrid insulating ferromagnet-topological insulator heterostructure devices. Appl. Phys. Lett.,2013,103: 202409.
[104]Carsten Timm. Transport through a quantum spin Hall quantum dot. Phys. Rev. B,2012,86:155456.
[105]Takehito Yokoyama, Yukio Tanaka, and Naoto Nagaosa. Anomalous magnetore-sistance of a two-dimensional ferromagnet/ferromagnet junction on the surface of a topological insulator. Phys. Rev. B,2010,81:121401(R).
[106]Gerson J. Ferreira and Daniel Loss. Magnetically Defined Qubits on 3D Topolog-ical Insulators. Phys. Rev. Lett.,2013,111:106802.
[107]Zhenhua Wu, F. M. Peeters, and Kai Chang. Electron tunneling through double magnetic barriers on the surface of a topological insulator. Phys. Rev. B,2010, 82:115211.
[108]Zhenhua Wu, F. M. Peeters, and Kai Chang. Spin and momentum filtering of electrons on the surface of a. topological insulator. Appl. Phys. Lett.,2011,98: 162101.
[109]R. Kubo. Statistical-Mechanical Theory of Irreversible Processes. I. General The-ory and Simple Applications to Magnetic and Conduction Problems. J. Phys. Soc. Jpn.,1957,12:570; Electron Transport in Metals and Solids. Can. J. Phys.,1956,34:1274.
[110]R. Landauer. Spatial Variation of Currents and Fields Due to Localized Scatterers in Metallic Conduction. IBM J. Res. Dev.,1957,1:223; Electrical resistance of disordered one-dimensional lattices. Philos. Mag.,1970,21:863.
[111]M. Buttiker, Y. Imry, R. Landauer and S. Pinhas. Generalized many-channel con-ductance formula with application to small rings. Phys. Rev. B,1985,31:6207; M. Buttiker. Four-Terminal Phase-Coherent Conductance. Phys. Rev. Lett., 1986.57:1761; Symmetry of electrical conduction. IBM J. Res. Dev.,1988, 32:317; Absence of backscattering in the quantum Hall effect in multiprobe con-ductors. Phys. Rev. B,1988,38:9375.
[112]L. R. Ram-Mohan, K. H. Yoo and R. L. Aggarwal. Transfer-matrix algorithm for the calculation of the band strueture of semiconduetor superlattices. Phys. Rev. B,1988,38:6151.
[113]Zhi-Yuan Li and Kai-Ming Ho. Application of structural symmetries in the plane-wave-based transfer-matrix method for three-dimensional photonic crystal waveg-uides. Phys. Rev. B,2003,68:245117.
[114]Jian-Bai Xia. Quantum waveguide theory for mesoscopic structures. Phys. Rev. B,1992,45:3593.
[115]P. S. Deo and A. M. Jayannavar. Quantum waveguide transport in serial stub and loop structures. Phys. Rev. B,1994,50:11629.
[116]B. S. Andereck and E. Abrahams. Numerical studies of inverse localisation length in one dimension. J. Phys. C,1980,13:L383.
[117]A. P. Jauho, N. S. Wingreen and Y. Meir. Time-dependent transport in interacting and noninteracting resonant-tunneling systems. Phys. Rev. B,1994,50:5528.
[118]Gerald D. Mahan. Many-Particle Physics. New York:Kluwer Academic/Plenum Publishers,2007.
[119]SUPRIYO DATTA. Electronic Transport in Mesoscopic Systems. New York:Cam-bridge University Press,1995.
[120]Yigal Meir, Ned S. Wingreen, and Patrick A. Lee. Transport through a Strongly Interacting Electron System:Theory of Periodic Conductance Oscillations. Phys. Rev. Lett.,1991,66:3048.
[121]M. Z. Hasan and C. L. Kane. Colloquium:Topological insulators. Rev. Mod. Phys.,2010,82:3045.
[122]A. A. Burkov and D. G. Hawthorn. Spin and Charge Transport on the Surface of a Topological Insulator. Phys. Rev. Lett.,2010,105:066802.
[123]Dimitrie Culcer, E. H. Hwang, Tudor D. Stanescu, and S. Das Sarma. Two-dimensional surface charge transport in topological insulators. Phys. Rev. B, 2010,82:155457.
[124]Liang Pu and C. L. Kane. Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator. Phys. Rev. Lett.,2008, 100:096407.
[125]Joel Moore. The next generation. Nat. Phys.,2009,5:378.
[126]D. Hsieh, Y. Xia, L. Wray, D. Qian, A. Pal, J. H. Dil, J. Osterwalder, F. Meier, G. Bihlmayer, C. L. Kane, Y. S. Hor, R. J. Cava, M. Z. Hasan. Observation of Unconventional Quantum Spin Textures in Topological Insulators. Science,2009, 323:919.
[127]Zhanybek Alpichshev, J. G. Analytis, J.-H. Chu, I. R. Fisher, Y. L. Chen, Z. X. Shen, A. Fang, and A. Kapitulnik. STM Imaging of Electronic Waves on the Surface of Bi2Te3:Topologically Protected Surface States and Hexagonal Warping Effects. Phys. Rev. Lett.,2010,104:016401.
[128]Peng Cheng, Canli Song, Tong Zhang, Yanyi Zhang, Yilin Wang, Jin-Feng Jia, Jing Wang, Yayu Wang Bang-Fen Zhu, Xi Chen, Xucun Ma, Ke He, Lili Wang, Xi Dai, Zhong Fang, Xincheng Xie, Xiao-Liang Qi, Chao-Xing Liu, Shou-Cheng Zhang, and Qi-Kun Xue. Landau Quantization of Topological Surface States in Bi2Se3. Phys. Rev. Lett.,2010,105:076801.
[129]Yuan Jian-Hui, Cheng Ze, Zhang Jian-Jun, Zeng Qi-Jun, and Zhang Jun-Pei. Charge transport and shot noise on the surface of a topological insulator with a magnetic modulation. Chin. Phys. B,2011,21:047203.
[130]Hosub Jin, Jung-Hwan Song, and Arthur J. Freeman. Dirac cone engineering in Bi2Se3 thin films. Phys. Rev. B,2011,83:125319.
[131]Rui Yu, Wei Zhang, Hai-Jun Zhang. Shou-Cheng Zhang, Xi Dai, Zhong Fang. Quantized Anomalous Hall Effect in Magnetic Topological Insulators. Science, 2010,329:61.
[132]Pouyan Ghaemi, Roger S. K. Mong, and J. E. Moore. In-Plane Transport and Enhanced Thermoelectric Performance in Thin Films of the Topological Insulators Bi2Te3 and Bi2Se3. Phys. Rev. Lett.,2010,105:166603.
[133]B. Seradjeh, J. E. Moore, and M. Franz. Exciton Condensation and Charge Frac-tionalization in a Topological Insulator Film. Phys. Rev. Lett.,2009,103: 066402.
[134]Huichao Li, L. Sheng, D. N. Sheng, and D. Y. Xing. Chern number of thin films of the topological insulator Bi2Se3. Phys. Rev. B,2010,82:165104.
[135]Wen-Yu Shan, Hai-Zhou Lu and Shun-Qing Shen. Effective continuous model for surface states and thin films of three-dimensional topological insulators. New J. Phys.,2010,12:043048.
[136]A. A. Zyuzin and A. A. Burkov. Thin topological insulator Blm in a perpendicular magnetic field. Phys. Rev. B,2011,83:195413.
[137]Huichao Li, L. Sheng, and D. Y. Xing. Quantum Hall effect in thin films of three-dimensional topological insulators. Phys. Rev. B,2011,84:035310.
[138]J. Chen, H. J. Qin, F. Yang, J. Liu, T. Guan, F. M. Qu, G. H. Zhang, J. R. Shi, X. C. Xie, C. L. Yang, K. H. Wu, Y. Q. Li, and L. Lu. Gate-Voltage Control of Chemical Potential and Weak Antilocalization in Bi2Se3. Phys. Rev. Lett. 2010.105:176602.
[139]Feng Zhai, and Peiyan Mu. Tunneling transport of electrons on the surface of a topological insulator attached with a spiral multiferroic oxide. Appl. Phys. Lett.,2011,98:022107.
[140]B. D. Kong, Y. G. Semenov, C. M. Krowne, and K. W. Kim. Unusual magne-toresistance in a topological insulator with a single ferromagnetic barrier. Appl. Phys. Lett.,2011,98:243112.
[141]Xiaoying Zhou, Huaihua Shao, Yiman Liu, Dongsheng Tang and Guanghui Zhou. Spatial distribution of spin polarization in a channel on the surface of a topological insulator. J. Phys.:Condens. Matter,2012,24:185301.
[142]Huaihua Shao, Xiaoying Zhou, Yuan Li, Genhua Liu and Guanghui Zhou. Spin polarization and charge transmission for a waveguide on surface of topological insulator. Appl. Phys. Lett.,2011,99:153104.
[143]Akinori Nishide, Alexey A. Taskin, Yasuo Takeichi, Taichi Okuda, Akito Kakizaki, Toru Hirahara, Kan Nakatsuji, Fumio Komori, Yoichi Ando, and Iwao Matsuda. Direct mapping of the spin-filtered surface bands of a three-dimensional quantum spin Hall insulator. Phys. Rev. B,2010,81:041309(R).
[144]R. B. Laughlin. Quantized Hall conductivity in two dimensions. Phys. Rev. B, 1981,23:5632.
[145]B. I. Halperin. Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential. Phys. Rev. B,1982,25:2185.
[146]M. P. Schwarz, M. A. Wilde, S. Groth, D. Grundler, Ch. Heyn, and D. Heitmann. Sawtoothlike de Haas-van Alphen oscillations of a two-dimensional electron sys-tem. Phys. Rev. B,2002,65:245315.
[147]X. F. Wang and P. Vasilopoulos. Magnetotransport in a two-dimensional electron gas in the presence of spin-orbit interaction. Phys. Rev. B,2003,67:085313.
[148]Zhigang Wang, Wei Zhang, and Ping Zhang. Magnetization in two-dimensional electron gas in a perpendicular magnetic fieid:The roles of edge states and spin-orbit coupling. Phys. Rev. B,2009,79:235327.
[149]Zhigang Wang, Zhen-Guo Fu, Shuang-Xi Wang, and Ping Zhang. Magnetic quan-tum oscillations for the surface states of topological insulator Bi2Se3. Phys. Rev. B,2010,82:085429.
[150]T. Hanaguri, K. Igarashi, M. Kawamura, H. Takagi, and T. Sasagawa. Momentum-resolved Landau-level spectroscopy of Dirac surface state in Bi2Se3. Phys. Rev. B,2010,82:081305(R).
[151]Zhihua Yang and Jung Hoon Han, Landau level states on a topological insulator thin film. Phys. Rev. B,2011,83:045415.
[152]Z. Papic, D. A. Abanin, Y. Barlas, and R. N. Bhatt. Tunable interactions and phase transitions in Dirac materials in a magnetic field. Phys. Rev. B,2011,84: 241306(R).
[153]M. M. Vazifeh and M. Franz. Spin response of electrons on the surface of a topo-logical insulator. Phys. Rev. B,2012,86:045451.
[154]Zhou Li and J. P. Carbotte, Magneto-optical conductivity in a topological insula-tor. Phys. Rev. B,2013,88:045414.
[155]V. P. Gusynin and S. G. Sharapov. Magnetic oscillations in planar systems with the Dirac-like spectrum of quasiparticle excitations. Phys. Rev. B,2005,71: 125124.
[156]P. Schwab and M. Dzierzawa. Landau levels in a topological insulator. Phys. Rev. B,2012,85:155403.
[157]Yoshinori Okada, Wenwen Zhou, Chetan Dhital, D. Walkup, Ying Ran, Z. Wang, Stephen D. Wilson, and V. Madhavan. Visualizing Landau Levels of Dirac Elec-trons in a One-Dimensional Potential. Phys. Rev. Lett.,2012,109:166407.
[158]Yan-Yang Zhang, Xiang-Rong Wang, and X C Xie. Three-dimensional topolog-iesl insulator in a magnetic field:chiral side surface states and quantized Hall conductance. J. Phys:Condens. Matter,2012,24:015004.
[159]Liang Fu. Hexagonal Warping Effects in the Surface States of the Topological Insulator Bi2Te3. Phys. Rev. Lett.,2009,103:266801.
[160]Degang Zhang and C. S. Ting. Impact of step defects on surface states of topo-logical insulators. Phys. Rev. B,2012,85:115434.
[161]Xiao-Liang Qi, Taylor L. Hughes, and Shou-Cheng Zhang. Topological field theory of time-reversal invariant insulators. Phys. Rev. B,2008,78:195424.
[162]Luis Brey and H. A. Fertig. Edge states and the quantized Hall effect in graphene. Phys. Rev. B,2006,73:195408.
[163]P. Vogt, P. De Padova, C. Quaresima, J. Avila, E. Frantzeskakis, M. C. Asensio, A. Resta, B. Ealet, and G. L. Lay. Silicene:Compelling Experimental Evidence for Graphenelike Two-Dimensional Silicon. Phys. Rev. Lett.,2012,108,155501.
[164]Chun-Liang Lin, Ryuichi Arafune, Kazuaki Kawahara, Noriyuki Tsukahara, Emi Minamitani, Yousoo Kim, Noriaki Takagi, and Maki Kawai. Structure of Silicene Grown on Ag(111). Appl. Phys. Express,2012,5:045802.
[165]Cheng-Cheng Liu, Wanxiang Feng, and Yugui Yao. Quantum Spin Hall Effect in Silicene and Two-Dimensional Germanium. Phys. Rev. Lett.,2011,107: 076802.
[166]Cheng-Cheng Liu, Hua Jiang, and Yugui Yao. Low-energy effective Hamiltonian involving spin-orbit coupling in silicene and two-dimensional germanium and tin. Phys. Rev. B,2011,84:195430.
[167]N. D. Drummond, V. Zolyomi, and V. I. Fal'ko. Electrically tunable band gap in silicene. Phys. Rev. B,2012,85:075423.
[168]Motohiko Ezawa. A topological insulator and helical zero mode in silicene under an inhomogeneous electric field. New J. Phys.,2012,14:033003.
[169]Motohiko Ezawa. Valley-Polarized Metals and Quantum Anomalous Hall Effect in Silicene. Phys. Rev. Lett.,2012,109:055502.
[170]Takehito Yokoyama. Controllable valley and spin transport in ferromagnetic sil-icene junctions. Phys. Rev. B,2013,87:241409(R).
[171]Shouting Huang, Wei Kang, and Li Yang. Electronic structure and quasiparticle bandgap of silicene structures. Appl. Phys. Lett.,2013,102:133106.
[172]Motohiko Ezawa. Photoinduced Topological Phase Transition and a Single Dirac-Cone State in Silicene. Phys. Rev. Lett.,2013,110:026603.
[173]K. Takeda and K. Shiraishi. Theoretical possibility of stage corrugation in Si and Ge analogs of graphite. Phys. Rev. B:1994,50:14916.
[174]S. Cahangirov, M. Topsakal, E. Akturk, H. Sahin, and S. Ciraci. Two-and One-Dimensional Honeycomb Structures of Silicon and Germanium. Phys. Rev. Lett.,2009,102:236804.
[175]Zeyuan Ni, Qihang Liu, Kechao Tang, Jiaxin Zheng, Jing Zhou, Rui Qin, Zhengx-iang Gao, Dapeng Yu, and Jing Lu. Tunable Bandgap in Silicene and Germanene. Nano Lett.,2011,12:113.
[176]Xing-Tao An, Yan-Yang Zhang, Jian-Jun Liu, and Shu-Shen Li. Quantum spin Hall effect induced by electric field in silicene. Appl. Phys. Lett.,2013,102: 043113.
[177]Xing-Tao An, Yan-Yang Zhang, Jian-Jun Liu and Shu-Shen Li. Measurable spin-polarized current in two-dimensional topological insulators. J. Phys.:Condens. Matter,2012,24:505602.
[178]Xing-Tao An, Yan-Yang Zhang, Jian-Jun Liu and Shu-Shen Li. Spin-polarized current induced by a local exchange field in a silicene nanoribbon. New J. Phys., 2012,14:083039.
[179]Wei-Feng Tsai, Cheng-Yi Huang, Tay-Rong Chang, Hsin Lin, Horng-Tay Jeng, and A. Bansil. Gated silicene as a tunable source of nearly 100% spin-polarized electrons. Nat. Commun.,2013,4:1500.
[180]A. Rycerz, J. Tworzydlo, and C.W. J. Beenakker. Valley filter and valley valve in graphene. Nat. Phys.,2007,3:172.
[181]Di Xiao, Wang Yao, and Qian Niu. Valley-Contrasting Physics in Graphene:Mag-netic Moment and Topological Transport. Phys. Rev. Lett.,2007,99,236809.
[182]A. R. Akhmerov, J. H. Bardarson, A. Rycerz, and C. W. J. Beenakker. Theory of the valley-valve effect in graphene nanoribbons. Phys. Rev. B,2008,77:205416.
[183]M. Tahir, A. Manchon, K. Sabeeh, and U. Schwingenschlogl. Quantum spin/valley Hall effect and topological insulator phase transitions in silicene. Appl. Phys. Lett.,2013,102:162412.
[184]C. J. Tabert and E. J. Nicol. AC/DC spin and valley Hall effects in silicene and germanene. Phys. Rev. B,2013,87:235426.
[185]Bumned Soodchomshom. Perfect spin-valley filter controlled by electric field in ferromagnetic silicene. J. Appl. Phys.,2014,115,023706.
[186]Ai Yamakage, Motohiko Ezawa, Yukio Tanaka, and Naoto Nagaosa. Charge trans-port in pn and npn junctions of silicene. Phys. Rev. B,2013.88:085322.
[187]Jun Ding, Zhenhua Qiao, Wanxiang Feng, Yugui Yao, and Qian Niu. Engineering quantum anomalous/valley Hall states in graphene via metal-atom adsorption:An ab-initio study. Phys. Rev. B,2011,84:195444.
[188]Havard Haugen, Daniel Huertas-Hernando, and Arne Brataas. Spin transport in proximity-induced ferromagnetic graphene. Phys. Rev. B,2008,77:115406.
[189]Adrian G. Swartz, Patrick M. Odenthal, Yufeng Hao, Rodney S. Ruoff, and Roland K. Kawakami. Integration of the Ferromagnetic Insulator EuO onto Graphene. ACS Nano,2012,6:10063.
[190]H. X. Yang, A. Hallal, D. Terrade, X. Waintal, S. Roche, and M. Chshiev. Proxim-ity Effects Induced in Graphene by Magnetic Insulators:First-Principles Calcu-lations on Spin Filtering and Exchange-Splitting Gaps. Phys. Rev. Lett.,2013, 110:046603.
[191]Takehito Yokoyarna, Yukio Tanaka, and Naoto Nagaosa. Anomalous magnetore-sistance of a two-dimensional ferromagnet/ferromagnet junction on the surface of a topological insulator. Phys. Rev. B,2010,81:121401(R).
[192]Peng Wei, Ferhat Katmis, Badih A. Assaf, Hadar Steinberg, Pablo Jarillo-Herrero, Donald Heiman, and Jagadeesh S. Moodera. Exchange-Coupling-Induced Symme-try Breaking in Topological Insulators. Phys. Rev. Lett.,2013,110:186807.
[2]S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, D. M. Treger. Spintronics:A Spin-Based Electronics Vision for the Future. Science,2001,294:1488.
[3]Igor. Zutic, Jaroslav. Fabian and S. Das Sarma. Spintronics:Fundamentals and applications. Rev. Mod. Phys.,2004,76:323.
[4]J. E. Hirsch. Spin Hall Effect. Phys. Rev. Lett.,1999,83:1834.
[5]Shuichi Murakami, Naoto Nagaosa, Shou-Cheng Zhang. Dissipationless Quantum Spin Current at Room Temperature. Science,2003,301:1348; Jairo Sinova, Dimitrie Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, and A. H. MacDonald. Universal Intrinsic Spin Hall Effect. Phys. Rev. Lett.,2004,92:126603.
[6]Y. K. Kato, R. C. Myers, A. C. Gossard, D. D. Awschalom. Observation of the Spin Hall Effect in Semiconductors. Science,2004,306:1910; J. Wunderlich, B. Kaestner, J. Sinova, and T. Jungwirth. Experimental Observation of the Spin-Hall Effect in a Two-Dimensional Spin-Orbit Coupled Semiconductor System. Phys. Rev. Lett.,2004,94:047204.
[7]W. Kohn. Theory of the insulating state. Phys. Rev.,1964,133:A171.
[8]K. v. Klitzing, G. Dorda and M. Pepper. New Method for High-Accuracy De-termination of the Fine-Structure Constant Based on Quantized Hall Resistance. Phys. Rev. Lett.,1980,45:494.
[9]J. E. Avron, D. Osadchy, R. Seiler. A topological look at the Quantum Hall Effect. Phys. Today,2003,56:38.
[10]C. L. Kane and E. J. Mele. Quantum Spin Hall Effect in Graphene. Phys. Rev. Lett..2005,95:226801.
[11]B. Andrei Bernevig, Taylor L. Hughes, Shou-Cheng Zhang. Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells. Science,2006, 314:1757.
[12]Markus Konig, Steffen Wiedmann, Christoph Bruene, Andreas Roth, Hartmut Buhmann, Laurens W. Molenkamp, Xiao-Liang Qi, Shou-Cheng Zhang. Quantum Spin Hall insulator state in HgTe Quantum Wells. Science,2007,318:766.
[13]Shuichi Murakami. Quantum Spin Hall Effect and Enhanced Magnetic Response by Spin-Orbit Coupling. Phys. Rev. Lett.,2007,97:236805.
[14]Chaoxing Liu, Taylor L. Hughes, Xiao-Liang Qi, KangWang, and Shou-Cheng Zhang. Quantum Spin Hall Effect in Type-Ⅱ Semiconductors. Phys. Rev. Lett. 2008,100:236601.
[15]Atsuo Shitade, Hosho Katsura, Jan Kun, Xiao-Liang Qi, Shou-Cheng Zhang, and Naoto Nagaosa. Quantum Spin Hall Effect in a Transition Metal Oxide Na2-IrO3. Phys. Rev. Lett.,2009,102:256403.
[16]Ivan Knez and R. R. Du. Finite conductivity in mesoscopic Hall bars of inverted InAs/GaSb quantum wells. Phys. Rev. B,2010,81:201301.
[17]Xiao-Liang Qi and Shou-Cheng Zhang. The quantum spin Hall effect and topo-logical insulators. Phys. Today,2010,63:33.
[18]C. L. Kane and E. J. Mele. Z2 Topological Order and the Quantum Spin Hall Effect. Phys. Rev. Lett.,2005,95:146802.
[19]Charles L. Kane and Eugene J. Mele. A New Spin on the Insulating State. Science, 2006,314:1692.
[20]J. Barnas, A. Fuss, R. E. Camley, P. Griinberg, and W. Zinn. Novel magnetoresis-tance effect in layered magnetic structures:Theory and experiment. Phys. Rev. B,1990,42:8110; Gary A. Prinz. Magnetoelectronics. Science,1998,282:1660.
[21]S. S. P. Parkin, D. Mauri. Spin engineering:Direct determination of the Ruderman-Kittel-Kasuya-Yosida far-field range function in ruthenium. Phys. Rev. B,1991,44:7131.
[22]J. S. Moodera, Lisa R. Kinder, Terrilyn M. Wong, and R. Meservey. Large Magne-toresistance at Room Temperature in Ferromagnetic Thin Film Tunnel Junctions. Phys. Rev. Lett.,1994,74:3273.
[23]G. H. Koha, H. J. Kim, W. C. Jeong, J. H. Oh, J. H. Park, S. Y. Lee, G. T. Jeong, I. J. Hwang, T. W. Kim, J. E. Lee, S. O. Park, U. I. Jeong, H. S. Jeong, Kinam Kim. Fabrication of high performance 64 kb MRAM. J. of Magnetism and Magnetic Materials,2004,272:1941.
[24]S. Das Sarma, Jaroslav Fabian, Xuedong Hu, Igor Zutic. Spin electronics and spin computation. Solid State communications,2001,119:207.
[25]Supriyo Datta and Biswajit Das. Electronic analog of the elecro-optic modulator. Appl. Phys. Lett.,1990,56:665.
[26]H. Ohno. Making Nonmagnetic Semiconductor Ferromagnetic. Science,1998, 281:951.
[27]Jun-ichiro Inoue, Gerrit E. W. Bauer, Laurens W. Molenkamp. Suppression of the persistent spin Hall current by defect scattering. Phys. Rev. B,2004,70: 041303(R).
[28]L. Sheng, D. N. Sheng, and C. S. Ting. Spin-Hall Effect in Two-Dimensional Electron Systems with Rashba Spin-Orbit Coupling and Disorder. Phys. Rev. Lett.,2005,94:016602; D. N. Sheng, L. Sheng, Z. Y. Weng, and F. D. M. Haldane. Spin Hall effect and spin transfer in a disordered Rashba model. Phys. Rev. B,2005,72:153307.
[29]Xing-Tao An, Yan-Yang Zhang, Jian-Jun Liu, and Shu-Shen Li. Quantum spin Hall effect induced by electric field in silicene. Appl. Phys. Lett.,2013,102: 043113.
[30]A. H. Castro Neto, N. M. R. Peres, K. S. Novoselov and A. K. Geim. The electronic properties of graphene. Rev. Mod. Phys.,2009,81:109.
[31]P. R. Wallace. The Band Theory of Graphite. Phys. Rev.,1947,71:622.
[32]J. C. Slonczewski, P. R. Weiss. Band Structure of Graphite. Phys. Rev.,1958, 109:272.
[33]J. W. McClure. Analysis of Multicarrier Galvanomagnetic Data for Graphite. Phys. Rev.,1958,112:715.
[34]J. Gonzalez, F. Guinea, and M. A. H. Vozmediano. Unconventional Quasiparticle Lifetime in Graphite. Phys. Rev. Lett.,1996,77:3589.
[35]F. D. M. Haldane. Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly". Phys. Rev. Lett.,1988, 61:2015.
[36]K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov. Electric Field Effect in Atomically Thin Carbon Films. Science,2004,306:666; K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos and A. A. Firsov. Two-dimensional gas of massless Dirac fermions in graphene. Nature,2005,438: 197.
[37]Daniel Huertas-Hernando, F. Guinea, and Arne Brataas. Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps. Phys. Rev. B,2006, 74:155426.
[38]Hongki Min, J. E. Hill, N. A. Sinitsyn. B. R. Sahu, Leonard Kleinman, and A. H. MacDonald. Intrinsic and Rashba spin-orbit interactions in graphene sheets. Phys. Rev. B,2006,74:165310.
[39]J. C. Boettger, S. B. Trickey. First-principles calculation of the spin-orbit splitting in graphene. Phys. Rev. B,2007,75:121402.
[40]Yugui Yao, Fei Ye, Xiao-Liang Qi, Shou-Cheng Zhang, and Zhong Fang. Spin-orbit gap of graphene:First-principles calculations. Phys. Rev. B,2007,75:041401.
[41]M. Gmitra, S. Konschuh, C. Ertler, C. Ambrosch-Draxl, and J. Fabian. Band-structure topologies of graphene:Spin-orbit coupling effects from first principles. Phys. Rev. B,2009,80:235431.
[42]Liang Fu, C. L. Kane and E. J. Mele. Topological insulator in Three Dimensions. Phys. Rev. Lett.,2007,98:106803.
[43]J. E. Moore and L. Balents. Topological invariants of time-reversal-invariant band structures. Phys. Rev. B,2007,75:121306(R).
[44]Rahul Roy. Z2 classification of quantum spin Hall systems:An approach using time-reversal invariance. Phys. Rev. B,2009,79:195321.
[45]Liang Fu and C. L. Kane. Topological insulators with inversion symmetry. Phys. Rev. B,2007,76:045302.
[46]D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava and M. Z. Hasan. A topological Dirac insulator in a quantum spin Hall phase. Nature,2008,452: 970.
[47]F. Patthey, W.-D. Schneider, H. Micklitz. Photoemission study of the Bi(111) surface. Phys. Rev. B,1994,49:11293.
[48]S Agergaard, Ch Sodergaard, H Li, M B Nielsen, S V Hoffmann, Z Li and Ph Hofmann. The effect of reduced dimensionality on a semimetal: the electronic structure of the Bi(110) surface. New J. Phys.,2001,3:15.
[49]Christian R. Ast and Hartmut Hochst. Fermi Surface of Bi(111) Measured by Photoemission Spectroscopy. Phys. Rev. Lett.,2001,87:177602.
[50]Ph. Hofmann. The surfaces of bismuth:Structural and electronic properties. Prog. Surf. Sci.,2006,81:191.
[51]T. Hirahara, T. Nagao, I. Matsuda, G. Bihlmayer, E. V. Chulkov, Yu. M. Koroteev, P. M. Echenique, M. Saito, and S. Hasegawa. Role of Spin-Orbit Coupling and Hybridization Effects in the Electronic Structure of Ultrathin Bi Films. Phys. Rev. Lett.,2006,97:146803.
[52]Haijun Zhang, Chao-Xing Liu, Xiao-Liang Qi, Xi Dai, Zhong Fang and Shou-Cheng Zhang. Topological insulators in Bi2Se3,Bi2Te3 and Sb2Te.3 with a single Dirac cone on the surface. Nat. Phys.,2009,5:438.
[53]Y. Xia, D. Qian, D. Hsieh, L.Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava and M. Z. Hasan. Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Nat. Phys.,2009,5:398.
[54]Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, Z.-X. Shen. Experimental Realization of a Three-Dimensional Topological Insulator, Bi2Te3. Science,2009,325:178.
55] Chao-Xing Liu, Xiao-Liang Qi, HaiJun Zhang, Xi Dai, Zhong Fang, and Shou-Cheng Zhang. Model Hamiltonian for topological insulators. Phys. Rev. B,2010, 82:045122.
[56]D. Hsieh, Y. Xia, D. Qian, L. Wray, J. H. Dil, F. Meier, J. Osterwalder. L. Patthey, J. G. Checkelsky, N. P. Ong, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer. Y. S. Hor, R. J. Cava and M. Z. Hasan. A tunable topological insulator in the spin helical Dirac transport regime. Nautre,2009,460:1101.
[57]Pedram Roushan, Jungpil Seo, Colin V. Parker, Y. S. Hor, D. Hsieh, Dong Qian, Anthony Richardella, M. Z. Hasan, R. J. Cava and Ali Yazdani. Topological surface states protected from backscattering by chiral spin texture. Nautre(London), 2009,460:1106; Tong Zhang, Peng Cheng, Xi Chen, Jin-Feng Jia, Xucun Ma, Ke He, Lili Wang, Haijun Zhang, Xi Dai, Zhong Fang, Xincheng Xie, and Qi-Kun Xue. Experimental Demonstration of Topological Surface States Protected by Time-Reversal Symmetry. Phys. Rev. Lett.,2009,103:266803.
[58]J. Linder, T. Yokoyama,and A. Sudbo. Anomalous finite size effects on surface states in the topological insulator Bi2Se3. Phys. Rev. B,2009,80:205401.
[59]Chao-Xing Liu, HaiJun Zhang, Binghai Yan, Xiao-Liang Qi, Thomas Frauen-heim, Xi Dai, Zhong Fang and Shou-Cheng Zhang. Oscillatory crossover from two-dimensional to three-dimensional topological insulators. Phys. Rev. B,2010, 81:041307.
[60]Hai-Zhou Lu, Wen-Yu Shan, Wang Yao, Qian Niu, and Shun-Qing Shen. Massive Dirac fermions and spin physics in an ultrathin film of topological insulator. Phys. Rev. B,2010,81:115407.
[61]Wen-Yu Shan, Hai-Zhou Lu and Shun-Qing Shen. Effective continuous model for surface states and thin films of three-dimensional topological insulators. New J. Phys.,2010,12:043048.
[62]Yao-Yi Li, Guang Wang, Xie-Gang Zhu, Min-Hao Liu, Cun Ye, Xi Chen, Ya-Yu Wang, Ke He, Li-Li Wang, Xu-Cun Ma, Hai-Jun Zhang, Xi Dai, Zhong Fang, Xin-Cheng Xie, Ying Liu, Xiao-Liang Qi, Jin-Feng Jia, Shou-Cheng Zhang, and Qi-Kun Xue. Intrinsic topological insulator Bi2Te-3 thin films on Si and their thickness limit. Adv. Mater.,2010,22:4002.
[63]Guanhua Zhang, Huajun Qin, Jing Teng, Jiandong Guo, Qinlin Guo, Xi Dal, Zhong Fang, and Kehui Wu. Quintuple-layer epitaxy of thin films of topological insulator Bi2Se3. Appl. Phys. Lett.,2009,95:053114.
[64]Yusuke Sakamoto, Toru Hirahara, Hidetoshi Miyazaki, Shin-ichi Kimura, and Shuji Hasegawa. Spectroscopic evidence of a topological quantum phase transi-tion in ultrathin Bi2Se3 films. Phys. Rev. B,2010,81:165432.
[65]Yi Zhang, Ke He, Cui-Zu Chang, Can-Li Song, Li-Li Wang, Xi Chen, Jin-Feng Jia, Zhong Fang, Xi Dai, Wen-Yu Shan, Shun-Qing Shen, Qian Niu, Xiao-Liang Qi, Shou-Cheng Zhang, Xu-Cun Ma and Qi-Kun Xue. Crossover of the three-dimensional topological insulator Bi2Se3 to the two-dimensional limit. Nat. Phys.,2010,6:584.
[66]Toru Hirahara, Yusuke Sakamoto, Yasuo Takeichi, Hidetoshi Miyazaki, Shin-ichi Kimura, Iwao Matsuda, Akito Kakizaki, and Shuji Hasegawa. Anomalous trans-port in an n-type topological insulator ultrathin Bi2Se3 film. Phys. Rev. B,2010, 82:155309.
[67]Minhao Liu, Cui-Zu Chang, Zuocheng Zhang, Yi Zhang, Wei Ruan, Ke He, Li-li Wang, Xi Chen, Jin-Feng Jia, Shou-Cheng Zhang, Qi-Kun Xue, Xucun Ma, and Yayu Wang. Electron interaction-driven insulating ground state in Bi2Se3 topological insulators in the two-dimensional limit. Phys. Rev. B,2011,83: 165440.
[68]Jian Wang, Ashley M. DaSilva, Cui-Zu Chang, Ke He, J. K. Jain, Nitin Samarth, Xu-Cun Ma, Qi-Kun Xue, and Moses H. W. Chan. Evidence for electron-electron interaction in topologicalinsulator thin films. Phys. Rev. B,2011,83:245438.
[69]Boubekeur Lalmi, Hamid Oughaddou, Hanna Enriquez, Abdelkader Kara, Sebastien Vizzini, Benidicte Ealet, and Bernard Aufray. Epitaxial growth of a silicene sheet. Appl. Phys. Lett.,2010,97:223109.
[70]Rong Yang, Lianchang Zhang, Yi Wang, Zhiwen Shi, Dongxia Shi, Hongjun Gao, Enge Wang, and Guangyu Zhang. An Anisotropic Etching Effect in the Graphene Basal Plane. Adv. Mater.,2010,22:4014.
[71]Lei Liu, Yingli Zhang, Wenlong Wang, Changzhi Gu, Xuedong Bai, and Enge Wang. Nanosphere Lithography for the Fabrication of Ultranarrow Graphene Nanoribbons and On-Chip Bandgap Tuning of Graphene. Adv. Mater.,2011, 23:1246.
[72]Zhiwen Shi, Rong Yang, Lianchang Zhang, Yi Wang, Donghua Liu, Dongxia Shi, Enge Wang, and Guangyu Zhang. Patterning Graphene with Zigzag Edges by Self-Aligned Anisotropic Etching. Adv. Mater.,2011,23:3061.
[73]Jin Seok Lee, Sarah Brittman, Dong Yu, and Hongkun Park. Vapor-Liquid-Solid and Vapor-Solid Growth of Phase-Change Sb2Te3 Nanowires and Sb2Te3/GeTe Nanowire Heterostructures. J. Am. Chem. Soc.,2008,130:6252.
[74]Yuri M. Zuev, Jin Seok Lee, Clement Galloy, Hongkun Park, and Philip Kim. Di-ameter Dependence of the Transport Properties of Antimony Telluride Nanowires. Nano Lett.,2010,10,3037.
[75]Desheng Kong, Jason C. Randel, Hailin Peng, Judy J. Cha, Stefan Meister, Keji Lai, Yulin Chen, Zhi-Xun Shen, Hari C. Manoharan, and Yi Cui. Topological Insulator Nanowires and Nanoribbons. Nano Lett.,2010,10,329.
[76]Hailin Peng, Keji Lai, Desheng Kong, Stefan Meister, Yulin Chen, Xiao-Liang Qi, Shou-Cheng Zhang, Zhi-Xun Shen and Yi Cui. Aharonov-Bohm interference in topological insulator nanoribbons. Nature Mater.,2010,9:225.
[77]Hanna Lind, Sven Lidin, and Ulrich Haussermann. Structure and bonding proper-ties of (Bi2Se3)m(Bi2)n stacks by first-principles density functional theory. Phys. Rev. B,2005,72:184101.
[78]Desheng Kong, Wenhui Dang, Judy J. Cha, Hui Li, Stefan Meister, Hailin Peng, Zhongfan Liu, and Yi Cui. Few-Layer Nanoplates of Bi2Se3 and Bi2Te3 with Highly Tunable Chemical Potential. Nano Lett.,2010,10,2245.
[79]Faxian Xiu, Liang He, Yong Wang, Lina Cheng, Li-Te Chang, Murong Lang, Guan Huang, Xufeng Kou, Yi Zhou, Xiaowei Jiang, Zhigang Chen, Jin Zou, Alexandros Shailos and Kang L. Wang. Manipulating surface states in topological insulator nanoribbons. Nature Nanotech.,2011,6:216.
[80]A. Scherer and H. G. Craighead. Fabrication of small laterally patterned multiple quantum wells. Appl. Phys. Lett.,1986,49:1284.
[81]M. Mehta, D. Reuter, A. Melnikov, and A. D. Wieck. Focused ion beam implan-tation induced site-selective growth of InAs quantum dots. Appl. Phys. Lett. 2007,91:123108.
[82]Nae-Man Park, Chel-Jong Choi, Tae-Yeon Seong, and Seong-Ju Park. Quantum Confinement in Amorphous Silicon Quantum Dots Embedded in Silicon Nitride. Phys. Rev. Lett.,2001,86:1355.
[83]S. Fafard, K. Hinzer, S. Raymond, M. Dion, J. McCaffrey, Y. Feng, S. Charbon-neau. Red-Emitting Semiconductor Quantum Dot Lasers. Science,1996,274: 1.350.
[84]Kai Chang and Wen-Kai Lou. Helical Quantum States in HgTe Quantum Dots with Inverted Band Structures. Phys. Rev. Lett.,2011,106:206802.
[85]Sungjae Cho, Dohun Kim, Paul Syers, Nicholas P. Butch, Johnpierre Paglione, and Michael S. Fuhrer. Topological Insulator Quantum Dot with Tunable Barriers. Nano Lett.,2011,12,469.
[86]Arijit Kundu, Alex Zazunov, Alfredo Levy Yeyati, Thierry Martin, and Reinhold Egger. Energy spectrum and broken spin-surface locking in topological insulator quantum dots. Phys. Rev. B,2011,83:125429.
[87]C. S. Tang and C. S. Chu. Coherent quantum transport in narrow constrictions in the presence of a finite-range longitudinally polarized time-dependent field. Phys. Rev. B,1999,60:1830.
[88]A. Reynoso, Gonzalo Usaj, M. J. Sanchez, and C. A. Balseiro. Theory of edge states in systems with Rashba spin-orbit coupling. Phys. Rev. B,2004,70: 235344.
[89]Zhigang Wang, Wei Zhang, and Ping Zhang. Magnetization in two-dimensional electron gas in a perpendicular magnetic field:The roles of edge states and spin-orbit coupling. Phys. Rev. B,2009,79:235327.
[90]J. Milton Pereira, Jr., V. Mlinar, and F. M. Peeters. Confined states and direction-dependent transmission in graphene quantum wells. Phys. Rev. B,2006,74: 045424.
[91]J. Milton Pereira, Jr., F. M. Peeters, and P. Vasilopoulos. Magnetic interface states in graphene-based quantum wires. Phys. Rev. B,2007,75:125433.
[92]Takehito Yokoyama, Alexander V. Balatsky, and Naoto Xagaosa. Gate-Controlled One-Dimensional Channel on the Surface of a 3D Topological Insulator. Phys. Rev. Lett.,2010,104:246806.
[93]Mark Johnson, Brian R. Bennett, M. J. Yang, M. M. Miller and B. V. Shanabrook. Hybrid Hall effect device. Appl. Phys. Lett.,1997,71:974; V. Kubrak, A. Neumann, B. L. Gallagher, P. C. Main, M. Henini, C. H. Marrows2 and B. J. Hickey. Magneto-resistance and Hall magnetometry of single submicron ferromag-netic structures. J. Appl. Phys.,2000,87:5986.
[94]H. A. Carmona, A. K. Geim, A. Nogaret, P. C. Main, T.J. Foster, and M. Henini, S.P. Beaumont, M. G. Blamire. Two Dimensional Electrons in a Lateral Magnetic Superlattice. Phys. Rev. Lett.,1995,74:3009; P. D. Ye, D. Weiss, R.R. Ger-hardts, M. Seeger, K. von Klitzing, K. Eberl, and H. Nickel. Electrons in a Periodic Magnetic Field Induced by a Regular Array of Micromagnets. Phys. Rev. Lett., 1995,74:3013.
[95]A. Nogaret, S. J. Bending, and M. Henini. Resistance Resonance Effects through Magnetic Edge States. Phys. Rev. Lett.,2000,84:2231.
[96]K. S. Novoselov, A. K. Geim, S. V. Dubonos, Y. G. Cornelissens, F. M. Peeters, and J. C. Maan. Scattering of ballistic electrons at a mesoscopic spot of strong magnetic field. Phys. Rev. B,2002,65:233312.
[97]M. Cerchez, S. Hugger, and T. Heinzel. Effect of edge transmission and elastic scattering on the resistance of magnetic barriers:Experiment and theory. Phys. Rev. B,2007,75:035341.
[98]T. Ando, T. Nakashini, and R. Saito. Berry's Phase and Absence of Back Scatter-ing in Carbon Nanotubes. J. Phys. Soc. Jpn.,1998,67:2857.
[99]Vadim V. Cheianov and Vladimir I. Fal'ko. Phys. Rev. B,2006,74:041403.
[100]M. I. Katsnelson, K. S. Novoselov, and A. K. Geim. Chiral tunnelling and the Klein paradox in graphene. Nat. Phys.,2006,2:620.
[101]A. De Martino, L. Dell'Anna, and R. Egger. Magnetic Confinement of Massless Dirac Fermions in Graphene. Phys. Rev. Lett.,2007,98:066802.
[102]Su-Yang Xu, Madhab Neupane, Chang Liu, Duming Zhang, Anthony Richardella, L. AndrewWray, Nasser Alidoust, Mats Leandersson, Thiagarajan Balasubrama-nian, Jaime Sanchez-Barriga, Oliver Rader, Gabriel Landolt. Bartosz Slomski, Jan Hugo Dil, Jurg Osterwalder, Tay-Rong Chang, Horng-Tay Jeng, Hsin Lin, Arun Bansil, Nitin Samarth and M. Zahid Hasan. Hedgehog spin texture and Berry's phase tuning in a magnetic topological insulator. Nat. Phys.,2012,8:616.
[103]A. Kandala, A. Richardella, D. W. Rench, D. M. Zhang, T. C. Flanagan, and N. Samarthb. Growth and characterization of hybrid insulating ferromagnet-topological insulator heterostructure devices. Appl. Phys. Lett.,2013,103: 202409.
[104]Carsten Timm. Transport through a quantum spin Hall quantum dot. Phys. Rev. B,2012,86:155456.
[105]Takehito Yokoyama, Yukio Tanaka, and Naoto Nagaosa. Anomalous magnetore-sistance of a two-dimensional ferromagnet/ferromagnet junction on the surface of a topological insulator. Phys. Rev. B,2010,81:121401(R).
[106]Gerson J. Ferreira and Daniel Loss. Magnetically Defined Qubits on 3D Topolog-ical Insulators. Phys. Rev. Lett.,2013,111:106802.
[107]Zhenhua Wu, F. M. Peeters, and Kai Chang. Electron tunneling through double magnetic barriers on the surface of a topological insulator. Phys. Rev. B,2010, 82:115211.
[108]Zhenhua Wu, F. M. Peeters, and Kai Chang. Spin and momentum filtering of electrons on the surface of a. topological insulator. Appl. Phys. Lett.,2011,98: 162101.
[109]R. Kubo. Statistical-Mechanical Theory of Irreversible Processes. I. General The-ory and Simple Applications to Magnetic and Conduction Problems. J. Phys. Soc. Jpn.,1957,12:570; Electron Transport in Metals and Solids. Can. J. Phys.,1956,34:1274.
[110]R. Landauer. Spatial Variation of Currents and Fields Due to Localized Scatterers in Metallic Conduction. IBM J. Res. Dev.,1957,1:223; Electrical resistance of disordered one-dimensional lattices. Philos. Mag.,1970,21:863.
[111]M. Buttiker, Y. Imry, R. Landauer and S. Pinhas. Generalized many-channel con-ductance formula with application to small rings. Phys. Rev. B,1985,31:6207; M. Buttiker. Four-Terminal Phase-Coherent Conductance. Phys. Rev. Lett., 1986.57:1761; Symmetry of electrical conduction. IBM J. Res. Dev.,1988, 32:317; Absence of backscattering in the quantum Hall effect in multiprobe con-ductors. Phys. Rev. B,1988,38:9375.
[112]L. R. Ram-Mohan, K. H. Yoo and R. L. Aggarwal. Transfer-matrix algorithm for the calculation of the band strueture of semiconduetor superlattices. Phys. Rev. B,1988,38:6151.
[113]Zhi-Yuan Li and Kai-Ming Ho. Application of structural symmetries in the plane-wave-based transfer-matrix method for three-dimensional photonic crystal waveg-uides. Phys. Rev. B,2003,68:245117.
[114]Jian-Bai Xia. Quantum waveguide theory for mesoscopic structures. Phys. Rev. B,1992,45:3593.
[115]P. S. Deo and A. M. Jayannavar. Quantum waveguide transport in serial stub and loop structures. Phys. Rev. B,1994,50:11629.
[116]B. S. Andereck and E. Abrahams. Numerical studies of inverse localisation length in one dimension. J. Phys. C,1980,13:L383.
[117]A. P. Jauho, N. S. Wingreen and Y. Meir. Time-dependent transport in interacting and noninteracting resonant-tunneling systems. Phys. Rev. B,1994,50:5528.
[118]Gerald D. Mahan. Many-Particle Physics. New York:Kluwer Academic/Plenum Publishers,2007.
[119]SUPRIYO DATTA. Electronic Transport in Mesoscopic Systems. New York:Cam-bridge University Press,1995.
[120]Yigal Meir, Ned S. Wingreen, and Patrick A. Lee. Transport through a Strongly Interacting Electron System:Theory of Periodic Conductance Oscillations. Phys. Rev. Lett.,1991,66:3048.
[121]M. Z. Hasan and C. L. Kane. Colloquium:Topological insulators. Rev. Mod. Phys.,2010,82:3045.
[122]A. A. Burkov and D. G. Hawthorn. Spin and Charge Transport on the Surface of a Topological Insulator. Phys. Rev. Lett.,2010,105:066802.
[123]Dimitrie Culcer, E. H. Hwang, Tudor D. Stanescu, and S. Das Sarma. Two-dimensional surface charge transport in topological insulators. Phys. Rev. B, 2010,82:155457.
[124]Liang Pu and C. L. Kane. Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator. Phys. Rev. Lett.,2008, 100:096407.
[125]Joel Moore. The next generation. Nat. Phys.,2009,5:378.
[126]D. Hsieh, Y. Xia, L. Wray, D. Qian, A. Pal, J. H. Dil, J. Osterwalder, F. Meier, G. Bihlmayer, C. L. Kane, Y. S. Hor, R. J. Cava, M. Z. Hasan. Observation of Unconventional Quantum Spin Textures in Topological Insulators. Science,2009, 323:919.
[127]Zhanybek Alpichshev, J. G. Analytis, J.-H. Chu, I. R. Fisher, Y. L. Chen, Z. X. Shen, A. Fang, and A. Kapitulnik. STM Imaging of Electronic Waves on the Surface of Bi2Te3:Topologically Protected Surface States and Hexagonal Warping Effects. Phys. Rev. Lett.,2010,104:016401.
[128]Peng Cheng, Canli Song, Tong Zhang, Yanyi Zhang, Yilin Wang, Jin-Feng Jia, Jing Wang, Yayu Wang Bang-Fen Zhu, Xi Chen, Xucun Ma, Ke He, Lili Wang, Xi Dai, Zhong Fang, Xincheng Xie, Xiao-Liang Qi, Chao-Xing Liu, Shou-Cheng Zhang, and Qi-Kun Xue. Landau Quantization of Topological Surface States in Bi2Se3. Phys. Rev. Lett.,2010,105:076801.
[129]Yuan Jian-Hui, Cheng Ze, Zhang Jian-Jun, Zeng Qi-Jun, and Zhang Jun-Pei. Charge transport and shot noise on the surface of a topological insulator with a magnetic modulation. Chin. Phys. B,2011,21:047203.
[130]Hosub Jin, Jung-Hwan Song, and Arthur J. Freeman. Dirac cone engineering in Bi2Se3 thin films. Phys. Rev. B,2011,83:125319.
[131]Rui Yu, Wei Zhang, Hai-Jun Zhang. Shou-Cheng Zhang, Xi Dai, Zhong Fang. Quantized Anomalous Hall Effect in Magnetic Topological Insulators. Science, 2010,329:61.
[132]Pouyan Ghaemi, Roger S. K. Mong, and J. E. Moore. In-Plane Transport and Enhanced Thermoelectric Performance in Thin Films of the Topological Insulators Bi2Te3 and Bi2Se3. Phys. Rev. Lett.,2010,105:166603.
[133]B. Seradjeh, J. E. Moore, and M. Franz. Exciton Condensation and Charge Frac-tionalization in a Topological Insulator Film. Phys. Rev. Lett.,2009,103: 066402.
[134]Huichao Li, L. Sheng, D. N. Sheng, and D. Y. Xing. Chern number of thin films of the topological insulator Bi2Se3. Phys. Rev. B,2010,82:165104.
[135]Wen-Yu Shan, Hai-Zhou Lu and Shun-Qing Shen. Effective continuous model for surface states and thin films of three-dimensional topological insulators. New J. Phys.,2010,12:043048.
[136]A. A. Zyuzin and A. A. Burkov. Thin topological insulator Blm in a perpendicular magnetic field. Phys. Rev. B,2011,83:195413.
[137]Huichao Li, L. Sheng, and D. Y. Xing. Quantum Hall effect in thin films of three-dimensional topological insulators. Phys. Rev. B,2011,84:035310.
[138]J. Chen, H. J. Qin, F. Yang, J. Liu, T. Guan, F. M. Qu, G. H. Zhang, J. R. Shi, X. C. Xie, C. L. Yang, K. H. Wu, Y. Q. Li, and L. Lu. Gate-Voltage Control of Chemical Potential and Weak Antilocalization in Bi2Se3. Phys. Rev. Lett. 2010.105:176602.
[139]Feng Zhai, and Peiyan Mu. Tunneling transport of electrons on the surface of a topological insulator attached with a spiral multiferroic oxide. Appl. Phys. Lett.,2011,98:022107.
[140]B. D. Kong, Y. G. Semenov, C. M. Krowne, and K. W. Kim. Unusual magne-toresistance in a topological insulator with a single ferromagnetic barrier. Appl. Phys. Lett.,2011,98:243112.
[141]Xiaoying Zhou, Huaihua Shao, Yiman Liu, Dongsheng Tang and Guanghui Zhou. Spatial distribution of spin polarization in a channel on the surface of a topological insulator. J. Phys.:Condens. Matter,2012,24:185301.
[142]Huaihua Shao, Xiaoying Zhou, Yuan Li, Genhua Liu and Guanghui Zhou. Spin polarization and charge transmission for a waveguide on surface of topological insulator. Appl. Phys. Lett.,2011,99:153104.
[143]Akinori Nishide, Alexey A. Taskin, Yasuo Takeichi, Taichi Okuda, Akito Kakizaki, Toru Hirahara, Kan Nakatsuji, Fumio Komori, Yoichi Ando, and Iwao Matsuda. Direct mapping of the spin-filtered surface bands of a three-dimensional quantum spin Hall insulator. Phys. Rev. B,2010,81:041309(R).
[144]R. B. Laughlin. Quantized Hall conductivity in two dimensions. Phys. Rev. B, 1981,23:5632.
[145]B. I. Halperin. Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential. Phys. Rev. B,1982,25:2185.
[146]M. P. Schwarz, M. A. Wilde, S. Groth, D. Grundler, Ch. Heyn, and D. Heitmann. Sawtoothlike de Haas-van Alphen oscillations of a two-dimensional electron sys-tem. Phys. Rev. B,2002,65:245315.
[147]X. F. Wang and P. Vasilopoulos. Magnetotransport in a two-dimensional electron gas in the presence of spin-orbit interaction. Phys. Rev. B,2003,67:085313.
[148]Zhigang Wang, Wei Zhang, and Ping Zhang. Magnetization in two-dimensional electron gas in a perpendicular magnetic fieid:The roles of edge states and spin-orbit coupling. Phys. Rev. B,2009,79:235327.
[149]Zhigang Wang, Zhen-Guo Fu, Shuang-Xi Wang, and Ping Zhang. Magnetic quan-tum oscillations for the surface states of topological insulator Bi2Se3. Phys. Rev. B,2010,82:085429.
[150]T. Hanaguri, K. Igarashi, M. Kawamura, H. Takagi, and T. Sasagawa. Momentum-resolved Landau-level spectroscopy of Dirac surface state in Bi2Se3. Phys. Rev. B,2010,82:081305(R).
[151]Zhihua Yang and Jung Hoon Han, Landau level states on a topological insulator thin film. Phys. Rev. B,2011,83:045415.
[152]Z. Papic, D. A. Abanin, Y. Barlas, and R. N. Bhatt. Tunable interactions and phase transitions in Dirac materials in a magnetic field. Phys. Rev. B,2011,84: 241306(R).
[153]M. M. Vazifeh and M. Franz. Spin response of electrons on the surface of a topo-logical insulator. Phys. Rev. B,2012,86:045451.
[154]Zhou Li and J. P. Carbotte, Magneto-optical conductivity in a topological insula-tor. Phys. Rev. B,2013,88:045414.
[155]V. P. Gusynin and S. G. Sharapov. Magnetic oscillations in planar systems with the Dirac-like spectrum of quasiparticle excitations. Phys. Rev. B,2005,71: 125124.
[156]P. Schwab and M. Dzierzawa. Landau levels in a topological insulator. Phys. Rev. B,2012,85:155403.
[157]Yoshinori Okada, Wenwen Zhou, Chetan Dhital, D. Walkup, Ying Ran, Z. Wang, Stephen D. Wilson, and V. Madhavan. Visualizing Landau Levels of Dirac Elec-trons in a One-Dimensional Potential. Phys. Rev. Lett.,2012,109:166407.
[158]Yan-Yang Zhang, Xiang-Rong Wang, and X C Xie. Three-dimensional topolog-iesl insulator in a magnetic field:chiral side surface states and quantized Hall conductance. J. Phys:Condens. Matter,2012,24:015004.
[159]Liang Fu. Hexagonal Warping Effects in the Surface States of the Topological Insulator Bi2Te3. Phys. Rev. Lett.,2009,103:266801.
[160]Degang Zhang and C. S. Ting. Impact of step defects on surface states of topo-logical insulators. Phys. Rev. B,2012,85:115434.
[161]Xiao-Liang Qi, Taylor L. Hughes, and Shou-Cheng Zhang. Topological field theory of time-reversal invariant insulators. Phys. Rev. B,2008,78:195424.
[162]Luis Brey and H. A. Fertig. Edge states and the quantized Hall effect in graphene. Phys. Rev. B,2006,73:195408.
[163]P. Vogt, P. De Padova, C. Quaresima, J. Avila, E. Frantzeskakis, M. C. Asensio, A. Resta, B. Ealet, and G. L. Lay. Silicene:Compelling Experimental Evidence for Graphenelike Two-Dimensional Silicon. Phys. Rev. Lett.,2012,108,155501.
[164]Chun-Liang Lin, Ryuichi Arafune, Kazuaki Kawahara, Noriyuki Tsukahara, Emi Minamitani, Yousoo Kim, Noriaki Takagi, and Maki Kawai. Structure of Silicene Grown on Ag(111). Appl. Phys. Express,2012,5:045802.
[165]Cheng-Cheng Liu, Wanxiang Feng, and Yugui Yao. Quantum Spin Hall Effect in Silicene and Two-Dimensional Germanium. Phys. Rev. Lett.,2011,107: 076802.
[166]Cheng-Cheng Liu, Hua Jiang, and Yugui Yao. Low-energy effective Hamiltonian involving spin-orbit coupling in silicene and two-dimensional germanium and tin. Phys. Rev. B,2011,84:195430.
[167]N. D. Drummond, V. Zolyomi, and V. I. Fal'ko. Electrically tunable band gap in silicene. Phys. Rev. B,2012,85:075423.
[168]Motohiko Ezawa. A topological insulator and helical zero mode in silicene under an inhomogeneous electric field. New J. Phys.,2012,14:033003.
[169]Motohiko Ezawa. Valley-Polarized Metals and Quantum Anomalous Hall Effect in Silicene. Phys. Rev. Lett.,2012,109:055502.
[170]Takehito Yokoyama. Controllable valley and spin transport in ferromagnetic sil-icene junctions. Phys. Rev. B,2013,87:241409(R).
[171]Shouting Huang, Wei Kang, and Li Yang. Electronic structure and quasiparticle bandgap of silicene structures. Appl. Phys. Lett.,2013,102:133106.
[172]Motohiko Ezawa. Photoinduced Topological Phase Transition and a Single Dirac-Cone State in Silicene. Phys. Rev. Lett.,2013,110:026603.
[173]K. Takeda and K. Shiraishi. Theoretical possibility of stage corrugation in Si and Ge analogs of graphite. Phys. Rev. B:1994,50:14916.
[174]S. Cahangirov, M. Topsakal, E. Akturk, H. Sahin, and S. Ciraci. Two-and One-Dimensional Honeycomb Structures of Silicon and Germanium. Phys. Rev. Lett.,2009,102:236804.
[175]Zeyuan Ni, Qihang Liu, Kechao Tang, Jiaxin Zheng, Jing Zhou, Rui Qin, Zhengx-iang Gao, Dapeng Yu, and Jing Lu. Tunable Bandgap in Silicene and Germanene. Nano Lett.,2011,12:113.
[176]Xing-Tao An, Yan-Yang Zhang, Jian-Jun Liu, and Shu-Shen Li. Quantum spin Hall effect induced by electric field in silicene. Appl. Phys. Lett.,2013,102: 043113.
[177]Xing-Tao An, Yan-Yang Zhang, Jian-Jun Liu and Shu-Shen Li. Measurable spin-polarized current in two-dimensional topological insulators. J. Phys.:Condens. Matter,2012,24:505602.
[178]Xing-Tao An, Yan-Yang Zhang, Jian-Jun Liu and Shu-Shen Li. Spin-polarized current induced by a local exchange field in a silicene nanoribbon. New J. Phys., 2012,14:083039.
[179]Wei-Feng Tsai, Cheng-Yi Huang, Tay-Rong Chang, Hsin Lin, Horng-Tay Jeng, and A. Bansil. Gated silicene as a tunable source of nearly 100% spin-polarized electrons. Nat. Commun.,2013,4:1500.
[180]A. Rycerz, J. Tworzydlo, and C.W. J. Beenakker. Valley filter and valley valve in graphene. Nat. Phys.,2007,3:172.
[181]Di Xiao, Wang Yao, and Qian Niu. Valley-Contrasting Physics in Graphene:Mag-netic Moment and Topological Transport. Phys. Rev. Lett.,2007,99,236809.
[182]A. R. Akhmerov, J. H. Bardarson, A. Rycerz, and C. W. J. Beenakker. Theory of the valley-valve effect in graphene nanoribbons. Phys. Rev. B,2008,77:205416.
[183]M. Tahir, A. Manchon, K. Sabeeh, and U. Schwingenschlogl. Quantum spin/valley Hall effect and topological insulator phase transitions in silicene. Appl. Phys. Lett.,2013,102:162412.
[184]C. J. Tabert and E. J. Nicol. AC/DC spin and valley Hall effects in silicene and germanene. Phys. Rev. B,2013,87:235426.
[185]Bumned Soodchomshom. Perfect spin-valley filter controlled by electric field in ferromagnetic silicene. J. Appl. Phys.,2014,115,023706.
[186]Ai Yamakage, Motohiko Ezawa, Yukio Tanaka, and Naoto Nagaosa. Charge trans-port in pn and npn junctions of silicene. Phys. Rev. B,2013.88:085322.
[187]Jun Ding, Zhenhua Qiao, Wanxiang Feng, Yugui Yao, and Qian Niu. Engineering quantum anomalous/valley Hall states in graphene via metal-atom adsorption:An ab-initio study. Phys. Rev. B,2011,84:195444.
[188]Havard Haugen, Daniel Huertas-Hernando, and Arne Brataas. Spin transport in proximity-induced ferromagnetic graphene. Phys. Rev. B,2008,77:115406.
[189]Adrian G. Swartz, Patrick M. Odenthal, Yufeng Hao, Rodney S. Ruoff, and Roland K. Kawakami. Integration of the Ferromagnetic Insulator EuO onto Graphene. ACS Nano,2012,6:10063.
[190]H. X. Yang, A. Hallal, D. Terrade, X. Waintal, S. Roche, and M. Chshiev. Proxim-ity Effects Induced in Graphene by Magnetic Insulators:First-Principles Calcu-lations on Spin Filtering and Exchange-Splitting Gaps. Phys. Rev. Lett.,2013, 110:046603.
[191]Takehito Yokoyarna, Yukio Tanaka, and Naoto Nagaosa. Anomalous magnetore-sistance of a two-dimensional ferromagnet/ferromagnet junction on the surface of a topological insulator. Phys. Rev. B,2010,81:121401(R).
[192]Peng Wei, Ferhat Katmis, Badih A. Assaf, Hadar Steinberg, Pablo Jarillo-Herrero, Donald Heiman, and Jagadeesh S. Moodera. Exchange-Coupling-Induced Symme-try Breaking in Topological Insulators. Phys. Rev. Lett.,2013,110:186807.