Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-27T20:17:50.452Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  15 October 2014

Hongming Weng
Affiliation:
Institute of Physics, Chinese Academy of Sciences, China; [email protected]
Xi Dai
Affiliation:
Institute of Physics, Chinese Academy of Sciences, China; [email protected]
Zhong Fang
Affiliation:
Institute of Physics, Chinese Academy of Sciences, China; [email protected]
Get access

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.

Type
Research Article
Copyright
Copyright © Materials Research Society 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Hasan, M.Z., Kane, C.L., Rev. Mod. Phys. 82 (4), 3045 (2010).Google Scholar
Qi, X.L., Zhang, S.C., Rev. Mod. Phys. 83 (4), 1057 (2011).Google Scholar
Schnyder, A., Ryu, S., Furusaki, A., Ludwig, A., Phys. Rev. B: Condens. Matter 78 (19), 195125 (2008).Google Scholar
Wan, X., Turner, A.M., Vishwanath, A., Savrasov, S.Y., Phys. Rev. B: Condens. Matter 83, 205101 (2011).CrossRefGoogle Scholar
Xu, G., Weng, H., Wang, Z., Dai, X., Fang, Z., Phys. Rev. Lett. 107 (18), 186806 (2011).CrossRefGoogle Scholar
Burkov, A.A., Balents, L., Phys. Rev. Lett. 107 (12), 127205 (2011).Google Scholar
Burkov, A.A., Hook, M.D., Balents, L., Phys. Rev. B: Condens. Matter 84 (23), 235126 (2011).CrossRefGoogle Scholar
Zyuzin, A.A., Wu, S., Burkov, A.A., Phys. Rev. B: Condens. Matter 85 (16), 165110 (2012).Google Scholar
Young, S.M., Zaheer, S., Teo, J.C.Y., Kane, C.L., Mele, E.J., Rappe, A.M., Phys. Rev. Lett. 108 (14), 140405 (2012).Google Scholar
Wang, Z., Sun, Y., Chen, X.-Q., Franchini, C., Xu, G., Weng, H., Dai, X., Fang, Z., Phys. Rev. B: Condens. Matter 85 (19), 195320 (2012).CrossRefGoogle Scholar
Wang, Z., Weng, H., Wu, Q., Dai, X., Fang, Z., Phys. Rev. B: Condens. Matter 88 (12), 125427 (2013).Google Scholar
Fu, L., Kane, C.L., Phys. Rev. Lett. 100 (9), 096407 (2008).Google Scholar
Qi, X.-L., Hughes, T.L., Raghu, S., Zhang, S.-C., Phys. Rev. Lett. 102 (18), 187001 (2009).Google Scholar
Hor, Y.S., Williams, A.J., Checkelsky, J.G., Roushan, P., Seo, J., Xu, Q., Zandbergen, H.W., Yazdani, A., Ong, N.P., Cava, R.J., Phys. Rev. Lett. 104 (5), 057001 (2010).Google Scholar
Fu, L., Berg, E., Phys. Rev. Lett. 105 (9), 097001 (2010).Google Scholar
Klitzing, K.V., Dorda, G., Pepper, M., Phys. Rev. Lett. 45, 494 (1980).Google Scholar
Prange, R.E., Girvin, S.M., The Quantum Hall Effect (Springer-Verlag, New York, 1987).Google Scholar
Chern, S.-S., Ann. Math. 46 (4), 674 (1945).CrossRefGoogle Scholar
Thouless, D.J., Kohmoto, M., Nightingale, M.P., den Nijs, M., Phys. Rev. Lett. 49, 405 (1982).Google Scholar
Stone, M., Quantum Hall Effect (World Scientific, Singapore, 1992).Google Scholar
Haldane, F.D.M., Phys. Rev. Lett. 61, 2015 (1988).Google Scholar
Liu, C.-X., Qi, X.-L., Dai, X., Fang, Z., Zhang, S.-C., Phys. Rev. Lett. 101 (14), 146802 (2008).Google Scholar
Yu, R., Zhang, W., Zhang, H.-J., Zhang, S.-C., Dai, X., Fang, Z., Science 329 (5987), 61 (2010).Google Scholar
Chang, C.-Z., Zhang, J., Feng, X., Shen, J., Zhang, Z., Guo, M., Li, K., Ou, Y., Wei, P., Wang, L.-L., Ji, Z.-Q., Feng, Y., Ji, S., Chen, X., Jia, J., Dai, X., Fang, Z., Zhang, S.-C., He, K., Wang, Y., Lu, L., Ma, X.-C., Xue, Q.-K., Science 340 (6129), 167 (2013).Google Scholar
Kane, C.L., Mele, E.J., Phys. Rev. Lett. 95, 226801 (2005).Google Scholar
Kane, C.L., Mele, E.J., Phys. Rev. Lett. 95 (14), 146802 (2005).Google Scholar
Bernevig, B.A., Zhang, S.-C.Phys. Rev. Lett. 96 (10), 106802 (2006).Google Scholar
Bernevig, B.A., Hughes, T.L., Zhang, S.C., Science 314 (5806), 1757 (2006).Google Scholar
König, M., Wiedmann, S., Brüne, C., Roth, A., Buhmann, H., Molenkamp, L.W., Qi, X.-L., Zhang, S.-C., Science 318 (5851), 766 (2007).Google Scholar
Fu, L., Kane, C., Mele, E., Phys. Rev. Lett. 98 (10), 106803 (2007).CrossRefGoogle Scholar
Moore, J.E., Balents, L., Phys. Rev. B: Condens. Matter 75, 121306 (2007).Google Scholar
Roy, R., Phys. Rev. B: Condens. Matter 79 (19), 195322 (2009).CrossRefGoogle Scholar
Ando, Y., J. Phys. Soc. Jpn. 82 (10), 102001 (2013).Google Scholar
Zhang, H.-J., Liu, C.-X., Qi, X.-L., Deng, X.-Y., Dai, X., Zhang, S.-C., Fang, Z., Phys. Rev. B: Condens. Matter 80 (8), 085307 (2009).Google Scholar
Hsieh, D., Qian, D., Wray, L., Xia, Y., Hor, Y.S., Cava, R.J., Hasan, M.Z., Nature 452 (7190), 970 (2008).Google Scholar
Moore, J., Nat. Phys. 5 (6), 378 (2009).Google Scholar
Zhang, H., Liu, C.-X., Qi, X.-L., Dai, X., Fang, Z., Zhang, S.-C., Nat. Phys. 5 (6), 438 (2009).Google Scholar
Xia, Y., Qian, D., Hsieh, D., Wray, L., Pal, A., Lin, H., Bansil, A., Grauer, D., Hor, Y.S., Cava, R.J., Hasan, M.Z., Nat. Phys. 5 (6), 398 (2009).Google Scholar
Chen, Y.L., Analytis, J.G., Chu, J.-H., Liu, Z.K., Mo, S.-K., Qi, X.L., Zhang, H.J., Lu, D.H., Dai, X., Fang, Z., Zhang, S.C., Fisher, I.R., Hussain, Z., Shen, Z.-X., Science 325 (5937), 178 (2009).Google Scholar
Volovik, G.E., The Universe in a Helium Droplet (OUP, Oxford, UK, 2009).Google Scholar
Liu, Z.K., Zhou, B., Zhang, Y., Wang, Z.J., Weng, H., Prabhakaran, D., Mo, S.-K., Shen, Z.X., Fang, Z., Dai, X., Hussain, Z., Chen, Y.L., Science 343 (6173), 864 (2014).Google Scholar
Liu, Z.K., Jiang, J., Zhou, B., Wang, Z.J., Zhang, Y., Weng, H., Prabhakaran, D., Mo, S.-K., Peng, H., Dudin, P., Kim, T., Hoesch, M., Fang, Z., Dai, X., Shen, Z.X., Feng, D.L., Hussain, Z., Chen, Y.L., Nat. Mater 13 (7), 677 (2014).Google Scholar
Neupane, M., Xu, S., Sankar, R., Alidoust, N., Bian, G., Liu, C., Belopolski, I., Chang, T.-R., Jeng, H.-T., Lin, H., Bansil, A., Chou, F., Zahid Hasan, M., Nat. Commun. 5, 3786 (2014).CrossRefGoogle Scholar
Borisenko, S., Gibson, Q., Evtushinsky, D., Zabolotnyy, V., Buechner, B., Cava, R.J., Phys. Rev. Lett. 113 (2), 027603 (2014).Google Scholar
Martin, R.M., Electronic Structure: Basic Theory and Practical Methods. (Cambridge University Press, Cambridge, UK, 2004).Google Scholar
Berry, M.V., Proc. R. Soc. London, Ser. A 392, 45 (1984).Google Scholar
Wilczek, F., Shapere, A., Geometric Phases in Physics (World Scientific, Singapore, 1989), vol. 5.Google Scholar
Wannier, G.H., Phys. Rev. 52 (3), 191 (1937).Google Scholar
Wannier, G.H., Rev. Mod. Phys. 34 (4), 645 (1962).Google Scholar
Fu, L., Kane, C.L., Phys. Rev. B: Condens. Matter 74, 195312 (2006).Google Scholar
Soluyanov, A.A., Vanderbilt, D., Phys. Rev. B: Condens. Matter 83 (3), 035108 (2011).Google Scholar
Yu, R., Qi, X.L., Bernevig, A., Fang, Z., Dai, X., Phys. Rev. B: Condens. Matter 84, 075119 (2011).Google Scholar
Ringel, Z., Kraus, Y.E., Phys. Rev. B: Condens. Matter 83 (24), 245115 (2011).Google Scholar
Fu, L., Phys. Rev. Lett. 106, 106802 (2011).Google Scholar
Hsieh, T.H., Lin, H., Liu, J., Duan, W., Bansi, A., Fu, L., Nat. Commun. 3, 982 (2012).CrossRefGoogle Scholar
Fu, L., Kane, C., Phys. Rev. B: Condens. Matter 76 (4), 045302 (2007).Google Scholar
Fukui, T., Hatsugai, Y., J. Phys. Soc. Jpn. 76 (5), 053702 (2007).Google Scholar
Marzari, N., Vanderbilt, D., Phys. Rev. B: Condens. Matter 56, 12847 (1997).Google Scholar
Souza, I., Marzari, N., Vanderbilt, D., Phys. Rev. B: Condens. Matter 65 (3), 035109 (2001).Google Scholar
Wang, X., Yates, J., Souza, I., Vanderbilt, D., Phys. Rev. B: Condens. Matter 74 (19), 195118 (2006).Google Scholar
Yates, J., Wang, X., Vanderbilt, D., Souza, I., Phys. Rev. B: Condens. Matter 75 (19), 195121 (2007).Google Scholar
Yip, S., Handbook of Materials Modeling (Springer-Verlag, New York, 2007).Google Scholar
Harrison, W.A., Electronic Structure and the Properties of Solids: The Physics of the Chemical Bond (Dover Publications, New York, 1989).Google Scholar
Godfrin, E.M., J. Phys. Condens. Matter 3 (40), 7843 (1991).Google Scholar
López Sancho, M.P., López Sancho, J.M., Rubio, J., J. Phys. F: Met. Phys. 14 (5), 1205 (1984).Google Scholar
López Sancho, M.P., López Sancho, J.M., Rubio, J., J. Phys. F: Met. Phys. 15 (4), 851 (1985).Google Scholar
Dai, X., Hughes, T.L., Qi, X.-L., Fang, Z., Zhang, S.-C., Phys. Rev. B: Condens. Matter 77, 125319 (2008).Google Scholar
Zhang, H., Zhang, S.-C., Phys. Status Solidi RRL 7 (12), 72 (2013).CrossRefGoogle Scholar
Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A.H., Ong, N.P., Rev. Mod. Phys. 82 (2), 1539 (2010).CrossRefGoogle Scholar
Qi, X.-L., Hughes, T.L., Zhang, S.-C., Phys. Rev. B: Condens. Matter 78, 195424 (2008).CrossRefGoogle Scholar
Van Vleck, J.H., The Theory of Electronic and Magnetic Susceptibilities (Oxford University Press, London, 1932).Google Scholar
Balents, L., Physics 4, 36 (2011).Google Scholar
Baltzer, P.K., Wojtowicz, P.J., Robbins, M., Lopatin, E., Phys. Rev. 151, 367 (1966).Google Scholar
Knez, I., Du, R.-R., Sullivan, G., Phys. Rev. Lett. 107, 136603 (2011).Google Scholar
Weng, H., Dai, X., Fang, Z., Phys. Rev. X 4, 011002 (2014).Google Scholar
Xu, Y., Yan, B., Zhang, H.-J., Wang, J., Xu, G., Tang, P., Duan, W., Zhang, S.-C., Phys. Rev. Lett. 111, 136804 (2013).Google Scholar
Si, C., Liu, J., Xu, Y., Wu, J., Gu, B.-L., Duan, W., Phys. Rev. B: Condens. Matter 89, 115429 (2014).Google Scholar
Song, Z., Liu, C.-C., Yang, J., Han, J., Ye, M., Fu, B., Yang, Y., Niu, Q., Lu, J., Yao, Y., Condens. Matter: Mater. Sci., published online February 2014 (available athttp://arXiv:1402.2399).Google Scholar
Liu, C.-C., Feng, W., Yao, Y., Phys. Rev. Lett. 107, 076802 (2011).Google Scholar
Neupert, T., Santos, L., Chamon, C., Mudry, C., Phys. Rev. Lett. 106 (23), 236804 (2011).Google Scholar
Tang, E., Mei, J.-W., Wen, X.-G., Phys. Rev. Lett. 106 (23), 236802 (2011).Google Scholar
Sun, K., Gu, Z., Katsura, H., Sarma, S.D., Phys. Rev. Lett. 106 (23), 236803 (2011).Google Scholar
Sheng, D.N., Gu, Z.-C., Sun, K., Sheng, L., Nat. Commun. 2, 389 (2011).Google Scholar
Levin, M., Stern, A., Phys. Rev. Lett. 103 (19), 196803 (2009).Google Scholar
Maciejko, J., Qi, X.-L., Karch, A., Zhang, S.-C., Phys. Rev. Lett. 105 (24), 246809 (2010).Google Scholar
Meng, Z.Y., Lang, T.C., Wessel, S., Assaad, F.F., Muramatsu, A., Nature 464 (7290), 847 (2010).Google Scholar
Pesin, D., Balents, L., Nat. Phys. 6 (5), 376 (2010).Google Scholar
Raghu, S., Qi, X.-L., Honerkamp, C., Zhang, S.-C., Phys. Rev. Lett. 100 (15), 156401 (2008).Google Scholar
Dzero, M., Sun, K., Galitski, V., Coleman, P., Phys. Rev. Lett. 104 (10), 106408 (2010).Google Scholar
Lu, F., Zhao, J.Z., Weng, H., Fang, Z., Dai, X., Phys. Rev. Lett. 110 (9), 096401 (2013).Google Scholar
Weng, H., Zhao, J., Wang, Z., Fang, Z., Dai, X., Phys. Rev. Lett. 112, 016403 (2014).Google Scholar
Deng, X.Y., Wang, L., Dai, X., Fang, Z., Phys. Rev. B: Condens. Matter 79 (7), 075114 (2009).Google Scholar
Gutzwiller, M.C., Phys. Rev. Lett. 10 (5), 159 (1963).Google Scholar
Gutzwiller, M.C., Phys. Rev. 134, A923 (1964).Google Scholar
Gutzwiller, M.C., Phys. Rev. 137, A1726 (1965).Google Scholar
Anisimov, V.I., Zaanen, J., Andersen, O.K., Phys. Rev. B: Condens. Matter 44, 943 (1991).Google Scholar
Lanatà, N., Strand, H.U.R., Dai, X., Hellsing, B., Phys. Rev. B: Condens. Matter 85, 035133 (2012).Google Scholar
Yao, Y.X., Wang, C.Z., Ho, K.M., Phys. Rev. B: Condens. Matter 83, 245139 (2011).Google Scholar
Qi, X.L., Li, R., Zang, J., Zhang, S.C., Science 323 (5918), 1184 (2009).Google Scholar
Wang, Z., Zhang, S.-C., Phys. Rev. X 2, 031008 (2012).Google Scholar
Wolgast, S., Kurdak, Ç., Sun, K., Allen, J.W., Kim, D.-J., Fisk, Z., Phys. Rev. B: Condens. Matter 88 (18), 180405 (2013).Google Scholar
Li, G., Xiang, Z., Yu, F., Asaba, T., Lawson, B., Cai, P., Tinsman, C., Berkley, A., Wolgast, S., Eo, Y.S., Kim, D.-J., Kurdak, C., Allen, J.W., Sun, K., Chen, X.H., Wang, Y.Y., Fisk, Z., Li, L., Condensed Matter: Strongly Correlated Electrons, published online June 2013 (available at arXiv.org/1306.5221).Google Scholar
Xu, N., Shi, X., Biswas, P.K., Matt, C.E., Dhaka, R.S., Huang, Y., Plumb, N.C., Radović, M., Dil, J.H., Pomjakushina, E., Conder, K., Amato, A., Salman, Z., Paul, D.M., Mesot, J., Ding, H., Shi, M., Phys. Rev. B: Condens. Matter 88 (12), 121102 (2013).Google Scholar
Neupane, M., Alidoust, N., Xu, S.-Y., Kondo, T., Kim, D.-J., Liu, C., Belopolski, I., Chang, T.-R., Jeng, H.-T., Durakiewicz, T., Condensed Matter: Strongly Correlated Electrons, published online June 2013 (available at arXiv.org/1306.4634).Google Scholar
Jiang, J., Li, S., Zhang, T., Sun, Z., Chen, F., Ye, Z.R., Xu, M., Ge, Q.Q., Tan, S.Y., Niu, X.H., Condensed Matter: Strongly Correlated Electrons, published online June 2013 (available at arXiv.org/1306.5664).Google Scholar
Yee, M.M., He, Y., Soumyanarayanan, A., Kim, D.-J., Fisk, Z., Hoffman, J.E., Condensed Matter: Strongly Correlated Electrons, published online August 2013 (available at arXiv.org/1308.1085).Google Scholar
Virot, F., Hayn, R., Richter, M., van den Brink, J., Phys. Rev. Lett. 106 (23), 236806 (2011).Google Scholar
Svane, A., Christensen, N.E., Cardona, M., Chantis, A.N., van Schilfgaarde, M., Kotani, T., Phys. Rev. B: Condens. Matter 84 (20), 205205 (2011).Google Scholar
Aryasetiawan, F., Gunnarsson, O., Rep. Prog. Phys. 61 (3), 237 (1998).Google Scholar
Kim, K., Jordan, K.D., J. Phys. Chem. 98 (40), 10089 (1994).Google Scholar
Heyd, J., Scuseria, G.E., Ernzerhof, M., J. Chem. Phys. 118 (18), 8207 (2003).Google Scholar
Tran, F., Blaha, P., Phys. Rev. Lett. 102 (22), 226401 (2009).Google Scholar
Slager, R.-J., Mesaros, A., Juričić, V., Zaanen, J., Nat. Phys. 9 (2), 98 (2013).Google Scholar
Hughes, T.L., Prodan, E., Bernevig, B.A., Phys. Rev. B: Condens. Matter 83 (24), 245132 (2011).Google Scholar
Jadaun, P., Xiao, D., Niu, Q., Banerjee, S.K., Phys. Rev. B: Condens. Matter 88 (8), 085110 (2013).Google Scholar
Turner, A.M., Zhang, Y., Mong, R.S.K., Vishwanath, A., Phys. Rev. B: Condens. Matter 85 (16), 165120 (2012).CrossRefGoogle Scholar