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

## Abstract

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.

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## Acknowledgements

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

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### Corresponding author

Correspondence to Shou-Cheng Zhang.

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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). https://doi.org/10.1038/nphys1270

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• DOI: https://doi.org/10.1038/nphys1270

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