Quantum Anomalous Hall Effects and Topological Phase Transitions in Silicene

Silicene is a monolayer of silicon atoms forming a two-dimensional honeycomb lattice, which is experimentally manufactured this year. The low energy theory is described by Dirac electrons, but they are massive due to a relatively large spin-orbit interaction. I will explain the following properties of silicene: 1) The band structure is controllable by applying an electric field [1]. Silicene undergoes a phase transition from a topological insulator to a band insulator by applying external electric field [1]. 2) The topological phase transition can be detected experimentally by way of diamagnetism [7]. 3) There is a novel circular dichroism and spinvalley selection rules by way of photon absorption [6]. 4) Silicene shows a quantum anomalous Hall effects when ferromagnet is attached onto silicone [3]. 5) Silicene shows a photo-induced quantum Hall effects when we apply strong laser onto silicene [8]. 6) Single Dirac cone state emerges when we apply photo-irradiation and electric field, where the gap is open at the K point and closed at the K' point [8].\\[4pt] [1] M. Ezawa, New J. Phys. 14, 033003 (2012).\\[0pt] [2] M. Ezawa, J. Phys. Jpn. 81, 064705 (2012). \\[0pt] [3] M. Ezawa, Phys. Rev. Lett. 109, 055502 (2012)\\[0pt] [4] M. Ezawa, Europhysics Letters 98, 67001 (2012).\\[0pt] [5] M. Ezawa, J. Phys. Soc. Jpn. 81, 104713 (2012).\\[0pt] [6] M. Ezawa, Phys. Rev. B 86, 161407(R) (2012).\\[0pt] [7] M. Ezawa, cond-mat/arXiv:1205.6541 (to be published in EPJB).\\[0pt] [8] M. Ezawa, cond-mat/arXiv:1207.6694.\\[0pt] [9] M. Ezawa, cond-mat/arXiv: 1209.2580.