中国学科发展战略·半导体物理学进展

半导体科学技术是事关提升国家竞争力的核心技术，几乎无处不在地发挥着其重要的作用。追溯历史，半导体科学技术之所以能成为当代如此重要的技术，正是 20 世纪四五十年代以来，国际上一些有远见卓识的科学家、企业家重视开展半导体物理研究的结果。以晶体管、集成电路和半导体激光器为代表的半导体科学技术引发了信息、通信和计算等领域的一场革命。同时，半导体物理研究也促进了整个凝聚态物理的大发展。20 世纪 80 年代以来，凝聚态物理研究在诸多方面取得了十分出色的研究成果。例如，整数、分数霍尔效应及后来的自旋霍尔效应、量子反常霍尔效应等的发现，拓扑绝缘体、马约拉纳费米子、外尔费米子等的发现。这些发现反映了科学家对固体中的新奇量子效应和元激发的新奇量子属性有了更为透彻的认识。半导体物理作为凝聚态物理的一个重要的分支学科，不仅参与了发现上述重要物理现象的过程，而且，事实上所发现的新奇量子效应和元激发的载体大多数本身就是半导体。然而，与凝聚态物理其他分支学科相比，半导体物理研究除了要有对新物理现象的探索外，还要有如何将所发现的新现象、新原理转化成新功能材料和器件的追求。事实上，关于这方面的探索研究是提升原始创新能力的关键。

我国半导体科学技术事业始于 20 世纪 50 年代。从 1956 年 4月起，科学规划委员会陆续集中 600 多位科学家和工程技术专家， 制定了《1956—1967 年科学技术发展远景规划纲要》，提出了《发展计算技术、半导体技术、无线电电子学、自动学和远距离操纵技术的紧急措施方案》。同时，高等教育部决定将北京大学、复旦大学、南京大学、厦门大学和东北人民大学（后来的吉林大学）有关专业的教师和学生集中到北京大学物理系，成立了中国第一个五校联合专门化班，由北京大学黄昆教授、复旦大学谢希德教授分别任主任和副主任，教授半导体物理课，开启了我国半导体物理的教学工作。同期间，他们合作撰写了我国第一部半导体物理学专著——《半导体物理学》，于 1958 年 8 月第一次正式出版，其后再版 6 次，到 2012 年 6 月被纳入“半导体科学与技术丛书”之一第七次再版。后来，为了适应半导体物理学自身的发展和教学授课的需要，北京大学叶良修教授于 1983 年 11 月出版了《半导体物理学》，该书多次再版，增添和细化了学科的教学内容。

20 世纪七八十年代，随着互补金属氧化物半导体（CMOS）微电子集成芯片和半导体激光器的问世，我国半导体事业也进入了快速发展期，开拓了不少新的领域，如光电子等。作为半导体科学技术创新源泉的半导体物理，本应得到更多的重视，但遗憾的是现实并非如此。我国固体物理学、半导体物理学的创始人黄昆先生 1977 年到中国科学院半导体研究所任所长以后不久就发现当时存在的这种不正常现象。他在 1990 年的回忆中就谈道：“在我国的一个很长时期内，形成了越有重要应用的学科，越是撇开基础研究不搞的不正常局面……”长期以来，这种现象造成了我国半导体科学技术缺乏原创动力。黄昆先生所指出的情况至今虽有所改善，但是依然存在。彻底扭转这种局面需要真正重视半导体物理的基础研究，同时要求从事半导体物理的研究队伍和从事半导体材料与器件的研究队伍在相互交叉的过程中形成合力，才有希望大幅度提升我国半导体科学技术的原始创新能力。

2014 年 2 月 8 日，中国科学院数学物理学部常委会十五届六次会议将“半导体物理”作为中国学科发展战略咨询项目上报中国科学院学部学术与出版工作委员会。2014 年 5 月 20 日，经国家自然科学基金委员会-中国科学院学科发展战略研究工作联合领导小组审议通过立项，同年 9 月 1 日咨询项目正式启动。

为期两年的学科发展战略研讨项目无疑是一项十分艰巨而又有重要意义的工作。为了确保半导体物理学科发展战略研讨的顺利进行，成立了由甘子钊、沈学础、陶瑞宝、于渌、朱邦芬、李树深、夏建白、高鸿钧等院士和郑厚植、常凯组成的顾问专家组，于 2014年 10 月 23 日和 24 日在北京西郊宾馆召开了项目组全体人员正式会议。会上由郑厚植院士介绍半导体物理进展战略规划立项背景及过程，并确定了如下原则：第一，半导体物理是没有国界的，要遵循学科在国际范围内的发展原貌，真实反映学科进展；第二，此次战略研究与今后的立项没有直接关联；第三，我们要从全局出发， 积极研讨，以高度的责任感来建议优先支持方向。

近 30 年来，无论是半导体物理学科发展的广度还是深度均超越了我们研究人员现有的认知。如果立足我们现有认知和研究工作去思考发展战略，很担心会出现“一叶障目”“王婆卖瓜”的错误导向。因此，我们一致认为发展战略研讨的要点首先是全面、充分地把握近 30 年来半导体物理学出现的新概念、新前沿、新突破以及它们可能引发的新机遇。

为此，我们提出了如下撰稿思路。第一，以传统半导体物理学科规划为框架；第二，以重要热点文章作为重要进展的源泉；第三，以国际半导体物理大会（ICPS）作为重要进展的风向标。这次战略研究是要介绍半导体物理在 30 年内的重要进展，要把握住所有涌现出的重要新概念、新理论，不回避半导体物理与其他凝聚态物理分支的交叉，但要在阐述重要学科交叉处展现半导体物理经久不息的生命力。同时，虽然我们不涉及半导体材料、器件学科的传统内容，但在介绍半导体新物理概念时会涉及新材料和新原理器件。

尽管如此，我们仍认为学科发展的战略决策不应由少数人来做选择和决策，我们所希望的是我国从事半导体物理的广大研究人员能从我们的战略研究报告中得到启示，寻找到他们的创新思路。

最后，经顾问专家组的认同，本书按如下十二章介绍近 30 年内半导体物理学的重大进展和展望。

第一章半导体能带理论由常凯撰写，第二章半导体声子物理由张俊、谭平恒撰写，第三章半导体中的杂质态、掺杂机制和单杂质态的量子调控由骆军委、邓惠雄、魏苏淮撰写，第四章一维、零维半导体结构中的量子现象由孙宝权、姬扬撰写，第五章光和物质的强相互作用由陈张海撰写，第六章半导体中的自旋量子现象由郑厚植、赵建华、张新惠、王开友撰写，第七章半导体 / 非半导体界面物理由郑厚植撰写，第八章半导体中的输运及其动力学过程由郑厚植撰写，第九章量子霍尔效应由李永庆撰写，第十章二维原子晶体及范德瓦耳斯异质结构由陈国瑞、张远波撰写，第十一章新概念半导体器件由郑厚植撰写，第十二章新测量技术由郑厚植、刘奇撰写。

国内 17 位有关方面的著名专家参与了具体的研讨和撰写工作， 包括复旦大学的陈张海、张远波、陈国瑞，北京计算科学研究中心的魏苏淮，中国科学院物理研究所的李永庆，中国科学院半导体研究所的常凯、张俊、谭平恒、骆军委、邓惠雄、孙宝权、姬扬、王开友、赵建华、张新惠、刘奇、郑厚植。凭着对半导体物理学科发展的关切和责任感，他们在承担繁重的科研任务的同时，为完成本咨询项目做出了重要的贡献。对此，我们深表谢意。

2016 年 6 月 4 日我们组织了“半导体物理学最新发展前沿”的专题研讨会，由常凯、杜瑞瑞、陈张海、贾金锋、李永庆、徐洪起教授分别做了专题报告《半导体微结构中人工规范场和新奇量子相》《基于 InAs/GaSb 量子阱的量子物态与拓扑量子计算平台》《半导体光学微腔中的激子极化激元》《拓扑绝缘体 / 超导体异质结中Majorana 费米子的观测》《半导体低维结构的量子输运性质》《固态半导体量子器件的构造及其量子信息技术中的应用》，并开展了研讨。这次专题研讨会开阔了战略研讨的视野。

鉴于半导体物理学日新月异的迅速发展，再加上受限于我们的时间、能力与知识，本书难免有许多不尽如人意的地方，敬请广大读者批评指正。

本书的出版得到中国科学院学部和国家自然科学基金委员会的联合支持，对此我们表示衷心的感谢！

　　郑厚植 常凯

　　2017 年 9 月 11 日

[1]Hohenberg P H. Kohn Inhomogeneous Electron Gas. Phys. Rev., 1964, 136: B864.

[2]Kohn W, Sham L J. Self-consistent equations including exchange and correlation effects. Physical Review, 1965, 140(4A):A1133-A1138.

[3]Van Schilfgaarde M , Kotani T, Faleev S. Quasiparticle self-consistent GW theory. Physical Review Letters, 2006, 96(22):226402.

[4]Onida G, Reining L, Rubio A. Electronic excitations: Density-functional versus many-body Green’s-function approaches. Rev. Mod. Phys. , 2002, 74 ：601.

[5]Surh M P, Northrup J E, Louie S G. Occupied quasiparticle bandwidth of potassium. Physical Review B, 1988, 38(9):5976.

[6]Koelling D D. Self-consistent energy band calculations. Reports on Progress in Physics, 1981, 44(2):140.

[7]Aryasetiawany F, Gunnarssonz O. The GW method.Rep. Prog. Phys., 1998, 61:237.

[8]Hedin L. New method for calculating the one-particle green’s function with application to the electron-gas problem. Physical Review, 1965, 139:A796.

[9]Aulbur W G, J？nsson L, Wilkins J W. Quasiparticle Calculations in Solids //Solid State Physics: Advances in Research and Applications.San Diego: Academic Press, 2000: 1-218.

[10]Rohlüng M, Krüger P, Pollmann J. Quasiparticle band-structure calculations for C, Si, Ge, GaAs, and SiC using Gaussian-orbital basis sets. Physical Review B, 1993, 48(24):17791- 17805.

[11]Hybertsen M S, Louie S G. Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies. Physical Review B (Condensed Matter), 1986, 34(8):5390.

[12]Hott R. GW-approximation energies and Hartree-Fock bands of semiconductors. Physical Review B (Condensed Matter), 1991, 44(3):1057-1065.

[13]Hybertsen M S, Louie S G. Model dielectric matrices for quasiparticle self-energy calculations.Physical Review B (Condensed Matter), 1988, 37(5):2733-2736.

[14]Li X Z, Gómezabal R, Jiang H, et al. Impact of widely used approximations to the G0W0 method: An all-electron perspective. New Journal of Physics, 2012, 14(4):23006-23026(21).

[15]Broido M M, Taylor J G. Bethe‐salpeter equation. Journal of Mathematical Physics, 1969, 10(1):184-209.

[16]Cammi R, Mennucci B, Tomasi J J. Fast evaluation of geometries and properties of excited molecules in solution: A tamm-dancoff model with application to 4-dimethylaminobenzonitrile. Journal of Physical Chemistry A, 2000, 104(23):5631-5637.

[17]Deslippe J, Samsonidze G, Strubbe D A, et al. Berkeley GW: A massively parallel computer package for the calculation of the quasiparticle and optical properties of materials and nanostructures. Computer Physics Communications, 2012, 183(6):1269-1289.

[18]Katsnelson M I, Irkhin V Y, Chioncel L, et al. Half-metallic ferromagnets: From band structure to many-body effects. Review of Modern Physics, 2008, 80(2): 315.

[19]Basov D N, Averitt R D, van Der Marel D, et al. Electrodynamics of correlated electron materials. Review of Modern Physics, 2011, 83(2): 471.

[20]Freysoldt C, Grabowski B, Hickel T, et al. First-principles calculations for point defects in solids. Review of Modern Physics, 2014, 86(1):253-305.

[21]Runge E, Gross E K U. Density-Functional theory for time-dependent systems. Phys. Rev. Lett. , 1984, 52:997.

[22]Ren J, Kaxiras E, Meng S. Optical properties of clusters and molecules from real-time time- dependent density functional theory using a self-consistent feld. Molecular Physics, 2010, 108(14):1829-1844.

[23]Meng S, Kaxiras E. Electron and hole dynamics in dye-sensitized solar cells: Influencing

factors and systematic trends. Nano Letters, 2010, 10(4):1238-1247.

[24]Born M, Oppenheimer R.Quantum theory of molecules. Ann. Phys. , 1927, 389:457.

[25]Feynman R P. Space-time approach to quantum electrodynamics. Physical Review, 1949, 76(6):769-789.

[26]Feynman R P, Hibbs A R. Quantum Mechanics and Path Integrals. New York: McGraw-Hill Inc, 1965, 91:1291-1301.

[27]Feynman R P. Atomic Theory of the Transition in Helium. Physical Review, 1953, 91(6):1291-1301.

[28]Li X Z, Wang E G. Computer Simulations of Molecules and Condensed Matters: from Electronic Structures to Molecular Dynamics. Beijing:Peking University Press, 2014.

[29]Chandler D, Wolynes P G. Exploiting the isomorphism between quantum theory and classical statistical mechanics of polyatomic fluids. Journal of Chemical Physics, 1981, 74(7):4078.

[30]Berne J B, Thirumalai D. On the simulation of quantum systems: Path integral methods. Annual Review of Physical Chemistry, 1986, 37(1):401-424.

[31]Ceperley D M. Path integrals in the theory of condensed helium. Reviews of Modern Physics, 1995, 67(2):279-355.

[32]Pollock E L, Ceperley D M. Path-integral computation of superfluid densities. Physical Review B (Condensed Matter), 1987, 36(16):8343.

[33]Tuckerman M E, Marx D, Klein M L, et al. Efficient and general algorithms for path integral

Car-Parrinello molecular dynamics. Journal of Chemical Physics, 1996, 104(14):5579-5588.

[34]Marx D, Parrinello M. Ab initio path integral molecular dynamics: Basic ideas.J. Chem. Phys, 1996, 104:4077.

[35]Tuckerman M E, Marx D, Parrinello M. The nature and transport mechanism of hydrated hydroxide ions in aqueous solution. Nature, 2002, 417:925.

[36]Li X Z, Probert M I, Alavi A, et al. Quantum nature of the proton in water-hydroxyl overlayers on metal surfaces. Physical Review Letters, 2010, 104(6):066102.

[37]Morales M A, Pierleoni C, Schwegler E, et al. Evidence for a first-order liquid-liquid transition in high-pressure hydrogen from ab initio simulations. Proceedings of the National Academy of Sciences of the United States of America, 2010, 107(29):12799-12803.

[38]Ceriotti M, Bussi G, Parrinello M. Nuclear quantum effects in solids using a colored-noise thermostat.Physical Review Letters, 2009, 103(3):030603.

[39]Porezag D, Frauenheim T, K？hler T, et al. Construction of tight-binding-like potentials on the basis of density-functional theory: Application to carbon. Physical Review B (Condensed Matter), 1995, 51(19):12947-12957.

[40]Slater J C, Koster G F. Simplified LCAO Method for the Periodic Potential Problem. Physical Review, 1954, 94(6):1498.

[41]Koskinen P, H,kkinen H, Seifert G, et al. Density-functional based tight-binding study of small gold clusters. New Journal of Physics, 2006, 8(40):6456-6460.

[42]K？hler C, Seifert G, Frauenheim T. Density functional based calculations for Fe n ( n ≤ 32).

Chemical Physics, 2005, 309(1):23-31.

[43]Th.Frauenheim, Weich F, Th.Kohler, et al. Density-functional-based construction of transferable nonorthogonal tight-binding potentials for Si and SiH. Phys.Rev.B, 1995, 52:11492.

[44]Guishan Zheng , H A W, Bobadovaparvanova P, et al. Parameter calibration of transition- metal elements for the spin-polarized self-consistent-charge density-functional tight-binding (DFTB) method: Sc, Ti, Fe, Co, and Ni. Journal of Chemical Theory & Computation, 2007, 3(4):1349-1367.

[45]Elstner M, Porezag D, Jungnickel G, et al. Self-consistent-charge density-functional tight- binding method for simulations of complex materials properties. Phys. Rev. B, 1998, 58:7260.

[46]K？hler C, Frauenheim T, Hourahine B, et al. Treatment of collinear and noncollinear electron spin within an approximate density functional based method. Journal of Physical Chemistry A, 2007, 111(26):5622-5629.

[47]Haugk M, Elsner J, Th F, et al. Structures, energetics and electronic properties of complex

III-V semiconductor systems. Physica Status Solidi, 2000, 217(1):473-511.

[48]Kohler C, Seifert G, Gerstmann U, et al. Approximate density-functional calculations of  spin densities in large molecular systems and complex solids. Physical Chemistry Chemical Physics, 2001, 3(23):5109-5114.

[49]Niehaus T A, Suhai S, Sala F D, et al. Tight-binding approach to time-dependent density- functional response theory. Physical Review B, 2001, 63(8):247-250.

[50]Niehaus T A, Rohlfing M, Della S F, et al. Quasiparticle energies for large molecules: A tight-binding-based Green’s-function approach. Physical Review A, 2005, 71(2):2508.

[51]Pecchia A, Carlo A D. Atomistic theory of transport in organic and inorganic nanostructures. Reports on Progress in Physics, 2004, 67(8):1497-1561.

[52]Elstner M, Hobza P, Frauenheim T, et al. Hydrogen bonding and stacking interactions of nucleic acid base pairs: A density-functional-theory based treatment. Journal of Chemical Physics, 2001, 114(12):5149-5155.

[53]Thouless D, Kohmoto M, Nightingale M, et al. Quantized hall conductance in a two- dimensional periodic potential. Phys. Rev. Lett. , 1982, 49:405.

[54]Haldane F D M. Model for a quantum hall effect without Landau levels: condensed-matter realization of the“parity anomaly”. Physical Review Letters, 1988, 61: 2015.

[55]Jackiw R. Fractional charge and zero modes for planar systems in a magnetic field. Phys.

Rev. D, 1984, 27: 2375.

[56]Kane C L, Mele E J. Quantum spin Hall effect in graphene. Physical Review Letters, 2005, 95(22):226801.

[57]Kane C L, Mele E J. Z2 topological order and the quantum spin Hall effect. Physical Review Letters, 2005, 95(14):146802.

[58]Bernevig B A, Hughes T L, Zhang S C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science, 2006, 314(5806):1757-1761.

[59]Liu C, Hughes T L, Qi X L, et al. Quantum spin Hall effect in inverted type-Ⅱ

semiconductors. Physical Review Letters, 2008, 100(23):236601.

[60]Du L, Knez I, Sullivan G. Robust Helical Edge Transport in Gated InAs/GaSb Bilayers. Phys. Rev. Lett. , 2005, 114: 096802.

[61]Miao M S, Yan Q, Lou W K, et al. Polarization-driven topological insulator transition in a GaN/InN/GaN quantum well. Physical Review Letters, 2012, 109(18): 186803.

[62]Zhou L, Dimakis E, Hathwar R, et al. Measurement and effects of polarization fields on one-

monolayer-thick InN/GaN multiple quantum wells. Physical Review B, 2013, 88:125310.

[63]Chadov S, Qi X, Kübler J, et al. Tunable multifunctional topological insulators in ternary

Heusler compounds. Nature Materials, 2010, 9(7):541-545.

[64]Dzero M, Sun K, Galitski V, et al. Topological kondo insulators. Physical Review Letters, 2010, 104(10):2909-2915.

[65]Qi X L, Hughes T L, Zhang S C. Topological invariants for the Fermi surface of a time- reversal-invariant superconductor. Physical Review B (Condensed Matter), 2010, 81(13):134508.

[66]Aidelsburger M, Atala M, Lohse M, et al. Realization of the hofstadter hamiltonian with ultracold atoms in optical lattices. Physical Review Letters, 2013, 111(18):185301.

[67]Hafezi M, Demler E A, Lukin M D, et al. Robust optical delay lines with topological protection. Nature Physics, 2012, 7(11):907-912.

[68]Haldane F , Raghu S. Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry. Phys. Rev. Lett. ,2008, 100: 013904; Wang Z, Chong Y, Joannopoulos J D,et al, Observation of unidirectional backscattering-immune topological electromagnetic states. Nature, 2009, 461: 772.

[69]Rechtsman M C, Zeuner J M, Tünnermann A, et al. Strain-induced pseudomagnetic field and

photonic Landau levels in dielectric structures. Nature Photonics, 2013, 7(2):153-158.

[70]Fang K, Yu Z, Fan S. Realizing effective magnetic field for photons by controlling the phase

of dynamic modulation. Nature Photonics, 2012, 6(11):782-787.

[71]Hafezi M, Rabl P. Optomechanically induced non-reciprocity in microring resonators. Optics Express, 2012, 20(7):7672-7684.

[72]Umucalilar R, Carusotto I.Artificial gauge field for photons in coupled cavity arrays. Phys.

Rev. A, 2011, 84: 043804.

[73]Khanikaev A B, Mousavi S H, Tse W K, et al. Photonic topological insulators. Nat. Mater. , 2013, 12: 233.

[74]Bernevig B, Zhang S C.Quantum spin hall effect. Phys. Rev. Lett. , 2006, 96: 106802.

[75]Hafezi M, Mittal S, Fan J, et al. Imaging topological edge states in silicon photonics. Nat. Photon. , 2013, 7: 1001.

[76]Rechtsman M, Zeuner J, Plotnik Y, et al. Photonic topological insulators. Nature Materials, 2013, 12(3):233-239.

[77]Yoshida S, Misawa S, Gonda S. Improvements on the electrical and luminescent properties of reactive molecular beam epitaxially grown GaN films by using AlN‐coated sapphire substrates. Applied Physics Letters, 1983, 42(5):427-429.

[78]Amano H, Sawaki N, Akasaki I. Metalorganic vapor phase epitaxial growth of a high quality

GaN film using an AIN buffer layer. Applied Physics Letters, 1986, 48(5):353-355.

[79]Asif Khan M, Van Hove J M, Kuznia J N, et al. High electron mobility GaN/AlxGa1-xN heterostructures grown by low‐pressure metalorganic chemical vapor deposition. Applied Physics Letters, 1991, 58(21):2408-2410.

[80]Ohtomo A, Hwang H Y. Corrigendum: A high-mobility electron gas at the LaAlO3/SrTiO3 heterointerface. Nature, 2004, 441(6973):423.

[81]Brinkman A, Huijben M, Zalk M V, et al. Magnetic effects at the interface between non- magnetic oxides. Nature Materials, 2007, 6(7):493-496.

[82]Reyren N, Thiel S, Caviglia A D, et al. Superconducting interfaces between insulating oxides. Science, 2007, 317(5842):1196-1199.

[83]Hwang H Y. Emergent phenomena at oxide interfaces. Nature Materials, 2012, 11(2):103- 113.

[84]Yoshikawa A, Che S B, Yamaguchi W, et al. Proposal and achievement of novel structure InN ∕ GaN multiple quantum wells consisting of 1 mL and fractional monolayer InN wells inserted in GaN matrix. Applied Physics Letters, 2007, 90(7):481.

[85]Miao M S, Yan Q, Lou W K, et al. Polarization-Driven Topological Insulator Transition in a GaN/InN/GaN Quantum Well. Physical Review Letters, 2012, 109(18):186803.

[86]Zhou L, Dimakis E, Hathwar R, et al. Measurement and effects of polarization fields on one-

monolayer-thick InN/GaN multiple quantum wells. Physical Review B, 2013, 88: 125310.

[87]Pan W, Dimakis E, Wang G T, et al. Two-dimensional electron gas in monolayer InN quantum wells.Appl. Phys. Lett., 2014, 105:213503.

[88]Zhang D, Lou W, Miao M, et al. Interface-induced topological insulator transition in GaAs/ Ge/GaAs quantum wells. Physical Review Letters, 2013, 111(15):156402.

[89]Zhang D, Zhang D B, Yang F, et al. Electronic and magneto-optical properties of monolayer phosphorene quantum dots. 2D Materials, 2015, 2:041001.

[90]Zhang H, Xu Y, Wang J, et al. Quantum spin hall and quantum anomalous hall states realized in junction quantum wells. Physical Review Letters, 2014, 112(21):216803.

[91]Zhang H, Wang J, Xu G, et al. Topological states in ferromagnetic CdO/EuO superlattices and quantum wells. Physical Review Letters, 2014, 112(9):096804.

[92]Liu Q , Zhang X, Abdalla L B, et al., Transforming common Ⅲ-Ⅴ and Ⅱ-Ⅵ semiconductor

compounds into topological heterostructures: The case of CdTe/InSb superlattices. Advanced Functional Materials, 2016, 26(19): 3259-3267.

[93]Liu Q, Zhang X, Abdalla L B, et al. Switching a normal insulator into a topological insulator

via electric field with application to phosphorene. Nano Letters, 2015, 15(2):1222.

[94]Bansil A, Lin H, Das T. Colloquium: Topological band theory. Reviews of Modern Physics, 2016, 88(2):021004.

[95]Ren Y, Qiao Z, Niu Q. Topological phases in two-dimensional materials: a review. Reports on Progress in Physics Physical Society, 2016, 79(6):066501.

[96]Gottlieb A D, Mauser N J. New measure of electron correlation. Physical Review Letters, 2005, 95(12):123003.

[97]Constantin L A, Fabiano E, Laricchia S, et al. Semiclassical neutral atom as a reference system in density functional theory. Physical Review Letters, 2011, 106(18):186406.

[98]Louis-Franfiois A, Alejandro L, O Anatole von L, et al.Machine learning for many-body physics: The case of the Anderson impurity model. Physical Review B, 2014, 90:155136.

[99]Lee J, Seko A, Shitara K, et al. Prediction model of band gap for inorganic compounds by combination of density functional theory calculations and machine learning techniques. Physical Review B, 2016, 93(11):115104.

[100]Pilania G, Mannodikanakkithodi A, Uberuaga B P, et al. Machine learning bandgaps of

double perovskites. Scientific Reports, 2016, 6:19375.