Skip to main content
SpringerLink
Log in

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

Frontiers of Physics volume 7, pages 175–192 (2012)Cite this article

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.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

References

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

    Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  34. M. P. Seah and W. A. Dench, Surface and Interface Analysis, 1979, 1: 2, http://dx.doi.org/10.1002/sia.740010103

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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

    Article  Google Scholar 

  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, http://dx.doi.org/10.1002/adma.201100678

    Article  Google Scholar 

  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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, UK

    Yulin Chen

  2. Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA, 94025, USA

    Yulin Chen

  3. Geballe Laboratory for Advanced Materials, Departments of Physics and Applied Physics, Stanford University, Stanford, CA, 94305, USA

    Yulin Chen

Authors
  1. Yulin Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yulin Chen.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Chen, Y. Studies on the electronic structures of three-dimensional topological insulators by angle resolved photoemission spectroscopy. Front. Phys. 7, 175–192 (2012). https://doi.org/10.1007/s11467-011-0197-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11467-011-0197-9

Keywords

search

Navigation