Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface


Topological insulators are new states of quantum matter in which surface states residing in the bulk insulating gap of such systems are protected by time-reversal symmetry. The study of such states was originally inspired by the robustness to scattering of conducting edge states in quantum Hall systems. Recently, such analogies have resulted in the discovery of topologically protected states in two-dimensional and three-dimensional band insulators with large spin–orbit coupling. So far, the only known three-dimensional topological insulator is BixSb1−x, which is an alloy with complex surface states. Here, we present the results of first-principles electronic structure calculations of the layered, stoichiometric crystals Sb2Te3, Sb2Se3, Bi2Te3 and Bi2Se3. Our calculations predict that Sb2Te3, Bi2Te3 and Bi2Se3 are topological insulators, whereas Sb2Se3 is not. These topological insulators have robust and simple surface states consisting of a single Dirac cone at the Γ point. In addition, we predict that Bi2Se3 has a topologically non-trivial energy gap of 0.3 eV, which is larger than the energy scale of room temperature. We further present a simple and unified continuum model that captures the salient topological features of this class of materials.

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

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Crystal structure.
Figure 2: Band structure, Brillouin zone and parity eigenvalues.
Figure 3: Band sequence.
Figure 4: Surface states.

Similar content being viewed by others


  1. Kane, C. L. & Mele, E. J. Quantum spin hall effect in graphene. Phys. Rev. Lett. 95, 226801 (2005).

    Article  ADS  Google Scholar 

  2. Bernevig, B. A. & Zhang, S. C. Quantum spin hall effect. Phys. Rev. Lett. 96, 106802 (2006).

    Article  ADS  Google Scholar 

  3. Kane, C. L. & Mele, E. J. Z2 topological order and the quantum spin hall effect. Phys. Rev. Lett. 95, 146802 (2005).

    Article  ADS  Google Scholar 

  4. Murakami, S. Quantum spin hall effect and enhanced magnetic response by spin–orbit coupling. Phys. Rev. Lett. 97, 236805 (2006).

    Article  ADS  Google Scholar 

  5. Bernevig, B. A., Hughes, T. L. & Zhang, S. C. Quantum spin hall effect and topological phase transition in HgTe quantum wells. Science 314, 1757–1761 (2006).

    Article  ADS  Google Scholar 

  6. König, M. et al. Quantum spin hall insulator state in HgTe quantum wells. Science 318, 766–770 (2007).

    Article  ADS  Google Scholar 

  7. Fu, L., Kane, C. L. & Mele, E. J. Topological insulators in three dimensions. Phys. Rev. Lett. 98, 106803 (2007).

    Article  ADS  Google Scholar 

  8. Moore, J. E. & Balents, L. Topological invariants of time-reversal-invariant band structures. Phys. Rev. B 75, 121306 (2007).

    Article  ADS  Google Scholar 

  9. Roy, R. On the Z2 classification of quantum spin hall models. Preprint at <> (2006).

  10. Qi, X.-L., Hughes, T. L. & Zhang, S.-C. Topological field theory of time-reversal invariant insulators. Phys. Rev. B 78, 195424 (2008).

    Article  ADS  Google Scholar 

  11. Dai, X., Hughes, T. L., Qi, X.-L., Fang, Z. & Zhang, S.-C. Helical edge and surface states in HgTe quantum wells and bulk insulators. Phys. Rev. B 77, 125319 (2008).

    Article  ADS  Google Scholar 

  12. Hsieh, D. et al. A topological dirac insulator in a quantum spin hall phase. Nature 452, 970–974 (2008).

    Article  ADS  Google Scholar 

  13. Fu, L. & Kane, C. L. Topological insulators with inversion symmetry. Phys. Rev. B 76, 045302 (2007).

    Article  ADS  Google Scholar 

  14. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    ADS  Google Scholar 

  15. Fang, Z. & Terakura, K. Structural distortion and magnetism in transition metal oxides: Crucial roles of orbital degrees of freedom. J. Phys. Condens. Matter 14, 3001–3014 (2002).

    Article  ADS  Google Scholar 

  16. Mishra, S. K., Satpathy, S. & Jepsen, O. Electronic structure and thermoelectric properties of bismuth telluride and bismuth selenide. J. Phys. Condens. Matter 9, 461–470 (1997).

    Article  ADS  Google Scholar 

  17. Larson, P. Effects of uniaxial and hydrostatic pressure on the valence band maximum in Sb2Te3: An electronic structure study. Phys. Rev. B 74, 205113 (2006).

    Article  ADS  Google Scholar 

  18. Black, J., Conwell, E. M., Seigle, L. & Spencer, C. W. Electrical and optical properties of some M2-N3-semiconductors. J. Phys. Chem. Solids 2, 240–251 (1957).

    Article  ADS  Google Scholar 

  19. Mooser, E. & Pearson, W. B. New semiconducting compounds. Phys. Rev. 101, 492–493 (1956).

    Article  ADS  Google Scholar 

  20. Wittel, K. & Manne, R. Atomic spin–orbit interaction parameters from spectral data for 19 elements. Theor. Chim. Acta 33, 347–349 (1974).

    Article  Google Scholar 

  21. Marzari, N. & Vanderbilt, D. Maximally localized generalized wannier functions for composite energy bands. Phys. Rev. B 56, 12847–12865 (1997).

    Article  ADS  Google Scholar 

  22. Souza, I., Marzari, N. & Vanderbilt, D. Maximally localized wannier functions for entangled energy bands. Phys. Rev. B 65, 035109 (2001).

    Article  ADS  Google Scholar 

  23. Sancho, M. P. L., Sancho, J. M. L. & Rubio, J. Quick iterative scheme for the calculation of transfer matrices: Application to Mo (100). J. Phys. F 14, 1205–1215 (1984).

    Article  ADS  Google Scholar 

  24. Sancho, M. P. L., Sancho, J. M. L., Sancho, J. M. L. & Rubio, J. Highly convergent schemes for the calculation of bulk and surface green functions. J. Phys. F 15, 851–858 (1985).

    Article  ADS  Google Scholar 

  25. Winkler, R. Spin–Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems (Springer Tracts in Modern Physics, Vol. 191, Springer, 2003).

    Book  Google Scholar 

  26. Koenig, M. et al. The quantum spin hall effect: Theory and experiment. J. Phys. Soc. Japan 77, 031007 (2008).

    Article  ADS  Google Scholar 

  27. Noh, H.-J. et al. Spin–orbit interaction effect in the electronic structure of Bi2Te3 observed by angle-resolved photoemission spectroscopy. Europhys. Lett. 81, 57006 (2008).

    Article  ADS  Google Scholar 

  28. Urazhdin, S. et al. Surface effects in layered semiconductors Bi2Se3 and Bi2Te3 . Phys. Rev. B 69, 085313 (2004).

    Article  ADS  Google Scholar 

  29. Xia, Y. et al. Electrons on the surface of Bi2Se3 form a topologically-ordered two dimensional gas with a non-trivial berry’s phase. Preprint at <> (2008).

  30. Qi, X.-L., Li, R.-D., Zang, J. & Zhang, S.-C. Inducing a magnetic monopole with topological surface states. Science 323, 1184–1187 (2009).

    Article  ADS  MathSciNet  Google Scholar 

Download references


We would like to thank B. F. Zhu for the helpful discussion. This work is supported by the NSF of China, the National Basic Research Program of China (No. 2007CB925000), the International Science and Technology Cooperation Program of China (No. 2008DFB00170) and by the US Department of Energy, Office of Basic Energy Sciences under contract DE-AC02-76SF00515.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Shou-Cheng Zhang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, H., Liu, CX., Qi, XL. et al. Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface. Nature Phys 5, 438–442 (2009).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing