Interview for Faculty Position

Three dimensional and two dimensional topological insulators of tetradymite semiconductors Bi₂Te₃, Bi₂Se₃, and Sb₂Te₃

Chao-Xing Liu

Physikalisches Institut (EP3) & Institute for Theoretical Physics and Astrophysics
University of Wurzburg

Topological insulators are new states of quantum matter with the surface states protected by time-reversal symmetry. In this talk, I would like to discuss about the realization of the three dimensional (3D) and two dimensional (2D) topological insulators in tetradymite semiconductors Bi₂Te₃, Bi₂Se₃, and Sb₂Te₃[1,2]. My talk is consisted of two parts. In the first part, I will consider about the 3D bulk materials and show that Sb₂Te₃, Bi₂Te₃ and Bi₂Se₃ are 3D topological insulators, while Sb₂Se₃ is not. Taking Bi₂Se₃ as an example, from ab initio calculation we find that an anti-crossing occurs between the conduction and valence band when the spin-orbit coupling is included, which gives us a hint of the existence of the topologically non-trivial phase. Based on the symmetry argument and k ⋅ p theory, an effective four band model is derived to described the low energy physics of the system. According to the four band model, we show that Bi₂Se₃ is a topological insulator with robust surface states consisting of a single Dirac cone. The interaction between magnetic impurities and surface states is also discussed. In the second part of my talk, I would like to discuss about the possible realization of 2D topological insulator with the Bi₂Se₃ and Bi₂Te₃ thin film. I will investigate the crossover regime from 3D to 2D topological insulators when the thickness of the film is reduced. Based on the four band effective model, we find that the crossover occurs in an oscillatory fashion as a function of the film thickness, alternating between topologically trivial and non-trivial two dimensional behavior. A physical picture is provided to understand the origin of the oscillation. Furthermore ab initio calculation is performed to study the realistic Bi₂Se₃ and Bi₂Te₃ thin film and confirm the analytical results.

[1] H. Zhang, C. Liu, X. Qi, X. Dai, Z. Fang, and S. Zhang, Nat Phys 5, 438 (2009).
[2] Chao-Xing Liu, HaiJun Zhang, Binghai Yan, Xiao-Liang Qi, Thomas Frauenheim, Xi Dai, Zhong Fang and Shou-Cheng Zhang, Phys. Rev. B 81, 041307(R) (2010).
[3] Qin Liu, Chao-Xing Liu, Cenke Xu, Xiao-Liang Qi, and Shou-Cheng Zhang, Phys. Rev. Lett. 102, 156603 (2009).