Studies on the electronic structures of three-dimensional topological insulators by angle resolved photoemission spectroscopy

Abstract

Three-dimensional (3D) topological insulators represent a new state of quantum matter with a bulk gap and odd number of relativistic Dirac fermions on the surface. The unusual surface states of topological insulators rise from the nontrivial topology of their electronic structures as a result of strong spin–orbital coupling. In this review, we will briefly introduce the concept of topological insulators and the experimental method that can directly probe their unique electronic structure: angle resolved photoemission spectroscopy (ARPES). A few examples are then presented to demonstrate the unique band structures of different families of topological insulators and the unusual properties of the topological surface states. Finally, we will briefly discuss the future development of topological quantum materials.

Keywords

topological insulator (TI) / photoemission / ARPES

References

[1] P. Anderson, Basic Notions of Condensed Matter Physics, Reading: Addison-Wesley, 1997

[2] K. v. Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett., 1980, 45: 494

[3] D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Phys. Rev. Lett., 1982, 49: 405

[4] J. Bellissard, A. van Elst, and H. Schulz-Baldes, J. Math. Phys., 1994, 35: 5373

[5] X. L. Qi and S. C. Zhang, Phys. Today, 2010, 63: 33

[6] L. Fu and C. L. Kane, Phys. Rev. B, 2007, 76: 045302

[7] X. L. Qi, T. L. Hughes, and S. C. Zhang, Phys. Rev. B, 2008, 78: 195424

[8] C. L. Kane and E. J. Mele, Phys. Rev. Lett., 2005, 95: 226801

[9] C. L. Kane and E. J. Mele, Phys. Rev. Lett., 2005, 95: 146802

[10] B. A. Bernevig, T. L. Hughes, and S. C. Zhang, Science, 2006, 314: 1757

[11] M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L. W. Molenkamp, X. L. Qi, and S. C. Zhang, Science, 2007, 318: 766

[12] D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Nature, 2008, 452: 970

[13] H. Zhang, C. Liu, X. Qi, X. Dai, Z. Fang, and S. Zhang, Nat. Phys., 2009, 5: 438

[14] Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. Hor, R. Cava, and M. Z. Hasan, Nat. Phys., 2009, 5: 398

[15] 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, Nature, 2009, 460: 1101

[16] 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, and Z. X. Shen, Science, 2009, 325: 178

[17] P. Roushan, J. Seo, C. V. Parker, Y. S. Hor, D. Hsieh, D. Qian, A. Richardella, M. Z. Hasan, R. J. Cava, and A. Yazdani, Nature, 2009, 460: 1106

[18] L. Fu, C. L. Kane, and E. J. Mele, Phys. Rev. Lett., 2007, 98: 106803

[19] L. Fu, Phys. Rev. Lett., 2009, 103: 266801

[20] A. R. Akhmerov, J. Nilsson, and C. W. J. Beenakker, Phys. Rev. Lett., 2009, 102: 216404

[21] J. E. Moore and L. Balents, Phys. Rev. B, 2007, 75: 121306

[22] R. Roy, Phys. Rev. B, 2009, 79: 195321

[23] X. L. Qi, T. L. Hughes, S. Raghu, and S. C. Zhang, Phys. Rev. Lett., 2009, 102: 187001

[24] L. Fu and E. Berg, Phys. Rev. Lett., 2010, 105: 097001

[25] Y. L. Chen, J. H. Chu, J. G. Analytis, Z. K. Liu, K. Igarashi, H. H. Kuo, X. L. Qi, S. K. Mo, R. G. Moore, D. H. Lu, M. Hashimoto, T. Sasagawa, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z. X. Shen, Science, 2010, 329: 659

[26] Y. Hor, J. Checkelsky, D. Qu, N. Ong, and R. Cava, J. Phys. Chem. Solids, 2011, 72: 572

[27] B. Yan, C. X. Liu, H. J. Zhang, C. Y. Yam, X. L. Qi, T. Frauenheim, and S. C. Zhang, Europhys. Lett., 2010, 90: 37002

[28] Y. L. Chen, Z. K. Liu, J. G. Analytis, J. H. Chu, H. J. Zhang, B. H. Yan, S. K. Mo, R. G. Moore, D. H. Lu, I. R. Fisher, S. C. Zhang, Z. Hussain, and Z. X. Shen, Phys. Rev. Lett., 2010, 105: 266401

[29] H. Min, J. E. Hill, N. A. Sinitsyn, B. R. Sahu, L. Kleinman, and A. H. MacDonald, Phys. Rev. B, 2006, 74: 165310

[30] Y. Yao, F. Ye, X. L. Qi, S. C. Zhang, and Z. Fang, Phys. Rev. B, 2007, 75: 041401

[31] H. Lin, R. S. Markiewicz, L. A. Wray, L. Fu, M. Z. Hasan, and A. Bansil, Phys. Rev. Lett., 2010, 105: 036404

[32] S. Chadov, X. Qi, J. Kübler, G. H. Fecher, C. Felser, and S. C. Zhang, Nat. Mater., 2010, 9: 541

[33] H. Lin, L. Wray, Y. Xia, S. Xu, S. Jia, R. Cava, A. Bansil, and M. Hasan, Nat. Mater., 2010, 9: 546

[34] M. P. Seah and W. A. Dench, Surface and Interface Analysis, 1979, 1: 2,

[35] A. Becquerel, CR (East Lansing, Mich.), 1839, 9: 561

[36] H. Hertz, Annalen der Physik, 1887, 267: 421

[37] A. Einstein, Ann. Phys., 1906, 20: 199

[38] B. Feuerbacher, B. Fitton, and R. Willis, Photoemission and The Electronic Properties of Surfaces, New York (London): Wiley, 1978

[39] A. Shitade, H. Katsura, J. Kunes, X. L. Qi, S. C. Zhang, and N. Nagaosa, Phys. Rev. Lett., 2009, 102: 256403

[40] X. Wan, A. M. Turner, A. Vishwanath, and S. Y. Savrasov, Phys. Rev. B, 2011, 83: 205101

[41] W. Röentgen, Sitzungsberichte der Physikalisch–Medizischen Gesellschaft in Wurzburg, Phys. Medi. Society, 1895, S. 132-141, Band 137

[42] A. J. Nicholson, Appl. Opt., 1970, 9: 1155

[43] F. Elder, A. Gurewitsch, R. Langmuir, and H. Pollock, Phys. Rev., 1947, 71: 829

[44] T. H. Maiman, Nature, 1960, 187: 493

[45] A. Lienard, L’ Eclairage Elec., 1898, 16: 5

[46] D. H. Bilderback, P. Elleaume, and E. Weckert, J. Phys. B, 2005, 38: S773

[47] E. Fermi, Zeits. f. Physik, 1934, 88: 172

[48] 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, and M. Z. Hasan, Science, 2009, 323: 919

[49] D. Hsieh, Y. Xia, D. Qian, L. Wray, F. Meier, J. H. Dil, J. Osterwalder, L. Patthey, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Phys. Rev. Lett., 2009, 103: 146401

[50] Z. Alpichshev, J. Analytis, J. Chu, I. Fisher, Y. Chen, Z. Shen, A. Fang, and A. Kapitulnik, Phys. Rev. Lett., 2010, 104: 16401

[51] S. Souma, K. Kosaka, T. Sato, M. Komatsu, A. Takayama, T. Takahashi, M. Kriener, K. Segawa, and Y. Ando, Phys. Rev. Lett., 2011, 106: 216803

[52] S.-Y. Xu, L. A. Wray, Y. Xia, F. von Rohr, Y. S. Hor, J. H. Dil, F. Meier, B. Slomski, J. Osterwalder, M. Neupane, H. Lin, A. Bansil, A. Fedorov, R. J. Cava, and M. Z. Hasan, arXiv: 1101.3985v1, 2011

[53] Y. Zhang, K. He, C. Z. Chang, C. L. Song, L. L. Wang, X. Chen, J. F. Jia, Z. Fang, X. Dai, W. Y. Shan, S.-Q. Shen, Q. Niu, X.-L. Qi, S.-C. Zhang, X.-C. Ma, and Q.-K. Xue, Nat. Phys., 2010, 6: 584

[54] C. X. Liu, H. Zhang, B. Yan, X. L. Qi, T. Frauenheim, X. Dai, Z. Fang, and S. C. Zhang, Phys. Rev. B, 2010, 81: 041307

[55] X. L. Qi, R. Li, J. Zang, and S. C. Zhang, Science, 2009, 323: 1184

[56] J. Zang and N. Nagaosa, Phys. Rev. B, 2010, 81: 245125

[57] F. Wilczek, Nature, 2009, 458: 129

[58] L. A. Wray, S.Y. Xu, Y. Xia, D. Hsieh, A. V. Fedorov, Y. S. Hor, R. J. Cava, A. Bansil, H. Lin, and M. Z. Hasan, Nat. Phys., 2011, 7: 32

[59] G. Wang, X. G. Zhu, Y. Y. Sun, Y. Y. Li, T. Zhang, J. Wen, X. Chen, K. He, L. L. Wang, X. C. Ma, J. F. Jia, S. B. Zhang, and Q. K. Xue, Adv. Mater., 2011, 23: 2929,

[60] J. G. Analytis, J. H. Chu, Y. Chen, F. Corredor, R. D. Mc-Donald, Z. X. Shen, and I. R. Fisher, Phys. Rev. B, 2010, 81: 205407

[61] R. A. Hein and E. M. Swiggard, Phys. Rev. Lett., 1970, 24: 53

[62] C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Rev. Mod. Phys., 2008, 80: 1083

[63] D. P. Spitzer and J. A. Sykes, J. Appl. Phys., 1966, 37: 1563

[64] K. Chrissafis, E. S. Vinga, K. M. Paraskevopoulos, and E. K. Polychroniadis, Physica Status Solidi (a), 2003, 196: 515

[65] K. Kurosaki, A. Kosuga, and S. Yamanaka, J. Alloys Comp., 2003, 351: 279

[66] K. Kurosaki, H. Uneda, H. Muta, and S. Yamanaka, J. Alloys Comp., 2004, 376: 43

[67] K. F. Hsu, S. Loo, F. Guo, W. Chen, J. S. Dyck, C. Uher, T. Hogan, E. K. Polychroniadis, and M. G. Kanatzidis, Science, 2004, 303: 818

[68] K. Hoang and S. D. Mahanti, Phys. Rev. B, 2008, 77: 205107

[69] J. Analytis, R. McDonald, S. Riggs, J. Chu, G. Boebinger, and I. Fisher, Nat. Phys., 2010, 6: 960

[70] Z. Ren, A. A. Taskin, S. Sasaki, K. Segawa, and Y. Ando, Phys. Rev. B, 2010, 82: 241306

[71] C. Brüne, C. X. Liu, E.G. Novik, E.M. Hankiewicz, H. Buhmann, Y. L. Chen, X. L. Qi, Z. X. Shen, S. C. Zhang, and L. W. Molenkamp, Phys. Rev. Lett., 2011, 106: 126803

[72] R. Yu, W. Zhang, H. J. Zhang, S. C. Zhang, X. Dai, and Z. Fang, Science, 2010, 329: 61

[73] F. Wilczek, Nat. Phys., 2009, 5: 614

[74] X. L. Qi, T. L. Hughes, and S. C. Zhang, Phys. Rev. B, 2010, 81: 134508

[75] A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, Phys. Rev. B, 2008, 78: 195125

[76] A. Nishide, A. A. Taskin, Y. Takeichi, T. Okuda, A. Kakizaki, T. Hirahara, K. Nakatsuji, F. Komori, Y. Ando, and I. Matsuda, Phys. Rev. B, 2010, 81: 041309(R)

[77] Y. Y. Li, G. Wang, X. G. Zhu, M. H. Liu, C. Ye, X. Chen, Y. Y. Wang, K. He, L. L. Wang, X. C. Ma, H. J. Zhang, X. Dai, Z. Fang, X. C. Xie, Y. Liu, X. L. Qi, J. F. Jia, S. C. Zhang, and Q. K. Xue, Adv. Mater., 2010, 22: 4002

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg