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Exploration and prediction of topological electronic materials based on first-principles calculations

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Abstract

The class of topological insulator materials is one of the frontier topics of condensed matter physics. The great success of this field is due to the conceptual breakthroughs in theories for topological electronic states and is strongly motivated by the rich variety of material realizations, thus making the theories testable, the experiments operable, and the applications possible. First-principles calculations have demonstrated unprecedented predictive power for material selection and design. In this article, we review recent progress in this field with a focus on the role of first-principles calculations. In particular, we introduce the Wilson loop method for the determination of topological invariants and discuss the band inversion mechanism for the selection of topological materials. Recent progress in quantum anomalous Hall insulators, large-gap quantum spin Hall insulators, and correlated topological insulators is also covered.

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References

  1. M.Z. Hasan, C.L. Kane, Rev. Mod. Phys. 82 (4), 3045 (2010).

    Google Scholar 

  2. X.L. Qi, S.C. Zhang, Rev. Mod. Phys. 83 (4), 1057 (2011).

    Google Scholar 

  3. A. Schnyder, S. Ryu, A. Furusaki, A. Ludwig, Phys. Rev. B: Condens. Matter 78 (19), 195125 (2008).

    Google Scholar 

  4. X. Wan, A.M. Turner, A. Vishwanath, S.Y. Savrasov, Phys. Rev. B: Condens. Matter 83, 205101 (2011).

    Google Scholar 

  5. G. Xu, H. Weng, Z. Wang, X. Dai, Z. Fang, Phys. Rev. Lett. 107 (18), 186806 (2011).

    Google Scholar 

  6. A.A. Burkov, L. Balents, Phys. Rev. Lett. 107 (12), 127205 (2011).

    Google Scholar 

  7. A.A. Burkov, M.D. Hook, L. Balents, Phys. Rev. B: Condens. Matter 84 (23), 235126 (2011).

    Google Scholar 

  8. A.A. Zyuzin, S. Wu, A.A. Burkov, Phys. Rev. B: Condens. Matter 85 (16), 165110 (2012).

    Google Scholar 

  9. S.M. Young, S. Zaheer, J.C.Y. Teo, C.L. Kane, E.J. Mele, A.M. Rappe, Phys. Rev. Lett. 108 (14), 140405 (2012).

    Google Scholar 

  10. Z. Wang, Y. Sun, X.-Q. Chen, C. Franchini, G. Xu, H. Weng, X. Dai, Z. Fang, Phys. Rev. B: Condens. Matter 85 (19), 195320 (2012).

    Google Scholar 

  11. Z. Wang, H. Weng, Q. Wu, X. Dai, Z. Fang, Phys. Rev. B: Condens. Matter 88 (12), 125427 (2013).

    Google Scholar 

  12. L. Fu, C.L. Kane, Phys. Rev. Lett. 100 (9), 096407 (2008).

    Google Scholar 

  13. X.-L. Qi, T.L. Hughes, S. Raghu, S.-C. Zhang, Phys. Rev. Lett. 102 (18), 187001 (2009).

    Google Scholar 

  14. Y.S. Hor, A.J. Williams, J.G. Checkelsky, P. Roushan, J. Seo, Q. Xu, H.W. Zandbergen, A. Yazdani, N.P. Ong, R.J. Cava, Phys. Rev. Lett. 104 (5), 057001 (2010).

    Google Scholar 

  15. L. Fu, E. Berg, Phys. Rev. Lett. 105 (9), 097001 (2010).

    Google Scholar 

  16. K.V. Klitzing, G. Dorda, M. Pepper, Phys. Rev. Lett. 45, 494 (1980).

    Google Scholar 

  17. R.E. Prange, S.M. Girvin, The Quantum Hall Effect (Springer-Verlag, New York, 1987).

    Google Scholar 

  18. S.-S. Chern, Ann. Math. 46 (4), 674 (1945).

    Google Scholar 

  19. D.J. Thouless, M. Kohmoto, M.P. Nightingale, M. den Nijs, Phys. Rev. Lett. 49, 405 (1982).

    Google Scholar 

  20. M. Stone, Quantum Hall Effect (World Scientific, Singapore, 1992).

    Google Scholar 

  21. F.D.M. Haldane, Phys. Rev. Lett. 61, 2015 (1988).

    Google Scholar 

  22. C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, S.-C. Zhang, Phys. Rev. Lett. 101 (14), 146802 (2008).

    Google Scholar 

  23. R. Yu, W. Zhang, H.-J. Zhang, S.-C. Zhang, X. Dai, Z. Fang, Science 329 (5987), 61 (2010).

    Google Scholar 

  24. C.-Z. Chang, J. Zhang, X. Feng, J. Shen, Z. Zhang, M. Guo, K. Li, Y. Ou, P. Wei, L.-L. Wang, Z.-Q. Ji, Y. Feng, S. Ji, X. Chen, J. Jia, X. Dai, Z. Fang, S.-C. Zhang, K. He, Y. Wang, L. Lu, X.-C. Ma, Q.-K. Xue, Science 340 (6129), 167 (2013).

    Google Scholar 

  25. C.L. Kane, E.J. Mele, Phys. Rev. Lett. 95, 226801 (2005).

    Google Scholar 

  26. C.L. Kane, E.J. Mele, Phys. Rev. Lett. 95 (14), 146802 (2005).

    Google Scholar 

  27. B.A. Bernevig, S.-C. Zhang Phys. Rev. Lett. 96 (10), 106802 (2006).

  28. B.A. Bernevig, T.L. Hughes, S.C. Zhang, Science 314 (5806), 1757 (2006).

    Google Scholar 

  29. M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L.W. Molenkamp, X.-L. Qi, S.-C. Zhang, Science 318 (5851), 766 (2007).

    Google Scholar 

  30. L. Fu, C. Kane, E. Mele, Phys. Rev. Lett. 98 (10), 106803 (2007).

    Google Scholar 

  31. J.E. Moore, L. Balents, Phys. Rev. B: Condens. Matter 75, 121306 (2007).

    Google Scholar 

  32. R. Roy, Phys. Rev. B: Condens. Matter 79 (19), 195322 (2009).

    Google Scholar 

  33. Y. Ando, J. Phys. Soc. Jpn. 82 (10), 102001 (2013).

    Google Scholar 

  34. H.-J. Zhang, C.-X. Liu, X.-L. Qi, X.-Y. Deng, X. Dai, S.-C. Zhang, Z. Fang, Phys. Rev. B: Condens. Matter 80 (8), 085307 (2009).

    Google Scholar 

  35. D. Hsieh, D. Qian, L. Wray, Y. Xia, Y.S. Hor, R.J. Cava, M.Z. Hasan, Nature 452 (7190), 970 (2008).

    Google Scholar 

  36. J. Moore, Nat. Phys. 5 (6), 378 (2009).

    Google Scholar 

  37. H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, S.-C. Zhang, Nat. Phys. 5 (6), 438 (2009).

    Google Scholar 

  38. Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y.S. Hor, R.J. Cava, M.Z. Hasan, Nat. Phys. 5 (6), 398 (2009).

    Google Scholar 

  39. 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, Science 325 (5937), 178 (2009).

    Google Scholar 

  40. G.E. Volovik, The Universe in a Helium Droplet (OUP, Oxford, UK, 2009).

    Google Scholar 

  41. Z.K. Liu, B. Zhou, Y. Zhang, Z.J. Wang, H. Weng, D. Prabhakaran, S.-K. Mo, Z.X. Shen, Z. Fang, X. Dai, Z. Hussain, Y.L. Chen, Science 343 (6173), 864 (2014).

    Google Scholar 

  42. Z.K. Liu, J. Jiang, B. Zhou, Z.J. Wang, Y. Zhang, H. Weng, D. Prabhakaran, S.-K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z.X. Shen, D.L. Feng, Z. Hussain, Y.L. Chen, Nat. Mater 13 (7), 677 (2014).

    Google Scholar 

  43. M. Neupane, S. Xu, R. Sankar, N. Alidoust, G. Bian, C. Liu, I. Belopolski, T.-R. Chang, H.-T. Jeng, H. Lin, A. Bansil, F. Chou, M. Zahid Hasan, Nat. Commun. 5, 3786 (2014).

    Google Scholar 

  44. S. Borisenko, Q. Gibson, D. Evtushinsky, V. Zabolotnyy, B. Buechner, R.J. Cava, Phys. Rev. Lett. 113 (2), 027603 (2014).

    Google Scholar 

  45. R.M. Martin, Electronic Structure: Basic Theory and Practical Methods. (Cambridge University Press, Cambridge, UK, 2004).

    Google Scholar 

  46. M.V. Berry, Proc. R. Soc. London, Ser. A 392, 45 (1984).

    Google Scholar 

  47. F. Wilczek, A. Shapere, Geometric Phases in Physics (World Scientific, Singapore, 1989), vol. 5.

  48. G.H. Wannier, Phys. Rev. 52 (3), 191 (1937).

    Google Scholar 

  49. G.H. Wannier, Rev. Mod. Phys. 34 (4), 645 (1962).

    Google Scholar 

  50. L. Fu, C.L. Kane, Phys. Rev. B: Condens. Matter 74, 195312 (2006).

    Google Scholar 

  51. A.A. Soluyanov, D. Vanderbilt, Phys. Rev. B: Condens. Matter 83 (3), 035108 (2011).

    Google Scholar 

  52. R. Yu, X.L. Qi, A. Bernevig, Z. Fang, X. Dai, Phys. Rev. B: Condens. Matter 84, 075119 (2011).

    Google Scholar 

  53. Z. Ringel, Y.E. Kraus, Phys. Rev. B: Condens. Matter 83 (24), 245115 (2011).

    Google Scholar 

  54. L. Fu, Phys. Rev. Lett. 106, 106802 (2011).

    Google Scholar 

  55. T.H. Hsieh, H. Lin, J. Liu, W. Duan, A. Bansi, L. Fu, Nat. Commun. 3, 982 (2012).

    Google Scholar 

  56. L. Fu, C. Kane, Phys. Rev. B: Condens. Matter 76 (4), 045302 (2007).

    Google Scholar 

  57. T. Fukui, Y. Hatsugai, J. Phys. Soc. Jpn. 76 (5), 053702 (2007).

    Google Scholar 

  58. N. Marzari, D. Vanderbilt, Phys. Rev. B: Condens. Matter 56, 12847 (1997).

    Google Scholar 

  59. I. Souza, N. Marzari, D. Vanderbilt, Phys. Rev. B: Condens. Matter 65 (3), 035109 (2001).

    Google Scholar 

  60. X. Wang, J. Yates, I. Souza, D. Vanderbilt, Phys. Rev. B: Condens. Matter 74 (19), 195118 (2006).

    Google Scholar 

  61. J. Yates, X. Wang, D. Vanderbilt, I. Souza, Phys. Rev. B: Condens. Matter 75 (19), 195121 (2007).

    Google Scholar 

  62. S. Yip, Handbook of Materials Modeling (Springer-Verlag, New York, 2007).

    Google Scholar 

  63. W.A. Harrison, Electronic Structure and the Properties of Solids: The Physics of the Chemical Bond (Dover Publications, New York, 1989).

    Google Scholar 

  64. E.M. Godfrin, J. Phys. Condens. Matter 3 (40), 7843 (1991).

    Google Scholar 

  65. M.P. López Sancho, J.M. López Sancho, J. Rubio, J. Phys. F: Met. Phys. 14 (5), 1205 (1984).

    Google Scholar 

  66. M.P. López Sancho, J.M. López Sancho, J. Rubio, J. Phys. F: Met. Phys. 15 (4), 851 (1985).

    Google Scholar 

  67. X. Dai, T.L. Hughes, X.-L. Qi, Z. Fang, S.-C. Zhang, Phys. Rev. B: Condens. Matter 77, 125319 (2008).

    Google Scholar 

  68. H. Zhang, S.-C. Zhang, Phys. Status Solidi RRL 7 (1–2), 72 (2013).

  69. N. Nagaosa, J. Sinova, S. Onoda, A.H. MacDonald, N.P. Ong, Rev. Mod. Phys. 82 (2), 1539 (2010).

    Google Scholar 

  70. X.-L. Qi, T.L. Hughes, S.-C. Zhang, Phys. Rev. B: Condens. Matter 78, 195424 (2008).

    Google Scholar 

  71. J.H. Van Vleck, The Theory of Electronic and Magnetic Susceptibilities (Oxford University Press, London, 1932).

    Google Scholar 

  72. L. Balents, Physics 4, 36 (2011).

    Google Scholar 

  73. P.K. Baltzer, P.J. Wojtowicz, M. Robbins, E. Lopatin, Phys. Rev. 151, 367 (1966).

    Google Scholar 

  74. I. Knez, R.-R. Du, G. Sullivan, Phys. Rev. Lett. 107, 136603 (2011).

    Google Scholar 

  75. H. Weng, X. Dai, Z. Fang, Phys. Rev. X 4, 011002 (2014).

    Google Scholar 

  76. Y. Xu, B. Yan, H.-J. Zhang, J. Wang, G. Xu, P. Tang, W. Duan, S.-C. Zhang, Phys. Rev. Lett. 111, 136804 (2013).

    Google Scholar 

  77. C. Si, J. Liu, Y. Xu, J. Wu, B.-L. Gu, W. Duan, Phys. Rev. B: Condens. Matter 89, 115429 (2014).

    Google Scholar 

  78. Z. Song, C.-C. Liu, J. Yang, J. Han, M. Ye, B. Fu, Y. Yang, Q. Niu, J. Lu, Y. Yao, Condens. Matter: Mater. Sci., published online February 2014 (available at http://arXiv:1402.2399).

  79. C.-C. Liu, W. Feng, Y. Yao, Phys. Rev. Lett. 107, 076802 (2011).

    Google Scholar 

  80. T. Neupert, L. Santos, C. Chamon, C. Mudry, Phys. Rev. Lett. 106 (23), 236804 (2011).

    Google Scholar 

  81. E. Tang, J.-W. Mei, X.-G. Wen, Phys. Rev. Lett. 106 (23), 236802 (2011).

    Google Scholar 

  82. K. Sun, Z. Gu, H. Katsura, S.D. Sarma, Phys. Rev. Lett. 106 (23), 236803 (2011).

    Google Scholar 

  83. D.N. Sheng, Z.-C. Gu, K. Sun, L. Sheng, Nat. Commun. 2, 389 (2011).

    Google Scholar 

  84. M. Levin, A. Stern, Phys. Rev. Lett. 103 (19), 196803 (2009).

    Google Scholar 

  85. J. Maciejko, X.-L. Qi, A. Karch, S.-C. Zhang, Phys. Rev. Lett. 105 (24), 246809 (2010).

    Google Scholar 

  86. Z.Y. Meng, T.C. Lang, S. Wessel, F.F. Assaad, A. Muramatsu, Nature 464 (7290), 847 (2010).

    Google Scholar 

  87. D. Pesin, L. Balents, Nat. Phys. 6 (5), 376 (2010).

    Google Scholar 

  88. S. Raghu, X.-L. Qi, C. Honerkamp, S.-C. Zhang, Phys. Rev. Lett. 100 (15), 156401 (2008).

    Google Scholar 

  89. M. Dzero, K. Sun, V. Galitski, P. Coleman, Phys. Rev. Lett. 104 (10), 106408 (2010).

    Google Scholar 

  90. F. Lu, J.Z. Zhao, H. Weng, Z. Fang, X. Dai, Phys. Rev. Lett. 110 (9), 096401 (2013).

    Google Scholar 

  91. H. Weng, J. Zhao, Z. Wang, Z. Fang, X. Dai, Phys. Rev. Lett. 112, 016403 (2014).

    Google Scholar 

  92. X.Y. Deng, L. Wang, X. Dai, Z. Fang, Phys. Rev. B: Condens. Matter 79 (7), 075114 (2009).

    Google Scholar 

  93. M.C. Gutzwiller, Phys. Rev. Lett. 10 (5), 159 (1963).

    Google Scholar 

  94. M.C. Gutzwiller, Phys. Rev. 134, A923 (1964).

    Google Scholar 

  95. M.C. Gutzwiller, Phys. Rev. 137, A1726 (1965).

    Google Scholar 

  96. V.I. Anisimov, J. Zaanen, O.K. Andersen, Phys. Rev. B: Condens. Matter 44, 943 (1991).

    Google Scholar 

  97. N. Lanatà, H.U.R. Strand, X. Dai, B. Hellsing, Phys. Rev. B: Condens. Matter 85, 035133 (2012).

    Google Scholar 

  98. Y.X. Yao, C.Z. Wang, K.M. Ho, Phys. Rev. B: Condens. Matter 83, 245139 (2011).

    Google Scholar 

  99. X.L. Qi, R. Li, J. Zang, S.C. Zhang, Science 323 (5918), 1184 (2009).

    Google Scholar 

  100. Z. Wang, S.-C. Zhang, Phys. Rev. X 2, 031008 (2012).

    Google Scholar 

  101. S. Wolgast, Ç. Kurdak, K. Sun, J.W. Allen, D.-J. Kim, Z. Fisk, Phys. Rev. B: Condens. Matter 88 (18), 180405 (2013).

    Google Scholar 

  102. G. Li, Z. Xiang, F. Yu, T. Asaba, B. Lawson, P. Cai, C. Tinsman, A. Berkley, S. Wolgast, Y.S. Eo, D.-J. Kim, C. Kurdak, J.W. Allen, K. Sun, X.H. Chen, Y.Y. Wang, Z. Fisk, L. Li, Condensed Matter: Strongly Correlated Electrons, published online June 2013 (available at arXiv.org/1306.5221).

  103. N. Xu, X. Shi, P.K. Biswas, C.E. Matt, R.S. Dhaka, Y. Huang, N.C. Plumb, M. Radović, J.H. Dil, E. Pomjakushina, K. Conder, A. Amato, Z. Salman, D.M. Paul, J. Mesot, H. Ding, M. Shi, Phys. Rev. B: Condens. Matter 88 (12), 121102 (2013).

    Google Scholar 

  104. M. Neupane, N. Alidoust, S.-Y. Xu, T. Kondo, D.-J. Kim, C. Liu, I. Belopolski, T.-R. Chang, H.-T. Jeng, T. Durakiewicz, Condensed Matter: Strongly Correlated Electrons, published online June 2013 (available at arXiv.org/1306.4634).

  105. J. Jiang, S. Li, T. Zhang, Z. Sun, F. Chen, Z.R. Ye, M. Xu, Q.Q. Ge, S.Y. Tan, X.H. Niu, Condensed Matter: Strongly Correlated Electrons, published online June 2013 (available at arXiv.org/1306.5664).

  106. M.M. Yee, Y. He, A. Soumyanarayanan, D.-J. Kim, Z. Fisk, J.E. Hoffman, Condensed Matter: Strongly Correlated Electrons, published online August 2013 (available at arXiv.org/1308.1085).

  107. F. Virot, R. Hayn, M. Richter, J. van den Brink, Phys. Rev. Lett. 106 (23), 236806 (2011).

    Google Scholar 

  108. A. Svane, N.E. Christensen, M. Cardona, A.N. Chantis, M. van Schilfgaarde, T. Kotani, Phys. Rev. B: Condens. Matter 84 (20), 205205 (2011).

    Google Scholar 

  109. F. Aryasetiawan, O. Gunnarsson, Rep. Prog. Phys. 61 (3), 237 (1998).

    Google Scholar 

  110. K. Kim, K.D. Jordan, J. Phys. Chem. 98 (40), 10089 (1994).

    Google Scholar 

  111. J. Heyd, G.E. Scuseria, M. Ernzerhof, J. Chem. Phys. 118 (18), 8207 (2003).

    Google Scholar 

  112. F. Tran, P. Blaha, Phys. Rev. Lett. 102 (22), 226401 (2009).

    Google Scholar 

  113. R.-J. Slager, A. Mesaros, V. Juričić, J. Zaanen, Nat. Phys. 9 (2), 98 (2013).

    Google Scholar 

  114. T.L. Hughes, E. Prodan, B.A. Bernevig, Phys. Rev. B: Condens. Matter 83 (24), 245132 (2011).

    Google Scholar 

  115. P. Jadaun, D. Xiao, Q. Niu, S.K. Banerjee, Phys. Rev. B: Condens. Matter 88 (8), 085110 (2013).

    Google Scholar 

  116. A.M. Turner, Y. Zhang, R.S.K. Mong, A. Vishwanath, Phys. Rev. B: Condens. Matter 85 (16), 165120 (2012).

    Google Scholar 

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Acknowledgments

We acknowledge support from the NSF of China and the 973 program of China (No. 2011CBA00108 and 2013CB921700).

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Weng, H., Dai, X. & Fang, Z. Exploration and prediction of topological electronic materials based on first-principles calculations. MRS Bulletin 39, 849–858 (2014). https://doi.org/10.1557/mrs.2014.216

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