Eur. Phys. J. B (2016) 89: 217
https://doi.org/10.1140/epjb/e2016-70374-1

Regular Article

Topological phases and phase transitions on the honeycomb lattice

¹ School of Zhangjiagang, Jiangsu University of Science and Technology, Zhangjiagang 215600, P.R. China
² National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, P.R. China

^a e-mail: yuanyangnju@126.com

Received: 13 June 2016
Received in final form: 19 July 2016
Published online: 5 October 2016

Abstract

We investigate possible phase transitions among the different topological insulators in a honeycomb lattice under the combined influence of spin-orbit couplings and staggered magnetic flux. We observe a series of topological phase transitions when tuning the flux amplitude, and find topologically nontrivial phases with high Chern number or spin-Chern number. Through tuning the exchange field, we also find a new quantum state which exhibits the electronic properties of both the quantum spin Hall state and quantum anomalous Hall state. The topological characterization based on the Chern number and the spin-Chern number are in good agreement with the edge-state picture of various topological phases.