Topological insulator is a new state of quantum matter, characterized by topological invariants. Exotic quantum phenomena, such as Majorana Fermions, magneto-electric effect, and quantum anomalous Hall effect, have been expected from topological insulators, while their experimental realizations remain challenging, due to the lack of suitable samples or requirement of extreme conditions. Within recent couple of years, more and more topological insulators were discovered, yet lots of new compounds still wait to be explored. On the other hand, the topological semimetal is a new topologically non-trivial state with Fermi points in the bulk and Fermi arcs on the surface. In this talk, I will start from our earlier predictions for Bi2Se3 family topological insulators, and discuss the characterization of topological nature from the Wannier representation and Willson loop method [1]. I then move to the recent study for the topological aspect and quantum magnetoresistance of Ag2Te [2]. The possible realization of quantized Anomalous Hall effect and Majorana fermions after breaking time reversal symmetry will be discussed from the view point of materials design [3,4]. Finally, I will discuss the Chern semimetal state in HgCr2Se4 [5].
References:
[1] R. Yu, X. L. Qi, A. Bernevig, Z. Fang, X. Dai, "An equivalent expression of Z2 topological invariant for band insulators using non-abelian berry's connection", arXiv:1101.2011 (2011).
[2] W. Zhang, R. Yu, W. X. Feng, Y. G. Yao, H. M. Weng, X. Dai, and Z. Fang, "Topological aspect and quantum magnetoresistance of Ag2Te", Phys. Rev. Lett. 106, 156808 (2011).
[3] R. Yu, W. Zhang, H.J. Zhang, S. C. Zhang, X. Dai, Z. Fang, "Quantized Anomalous Hall Effect in Magnetic Topological Insulators", Science 329, 61 (2010).
[4] H. M. Weng, G. Xu, H. J. Zhang, S. C. Zhang, X. Dai, Z. Fang, "Half-metallic surface states and topological superconductivity in NaCoO2" Phys. Rev. B 84, R060408 (2011).
[5] G. Xu, H. M. Weng, Z. J. Wang, X. Dai, and Z. Fang, "Chern semi-metal and quantized anomalous Hall effect in HgCr2Se4", Phys. Rev. Lett. (accepted, 2011).