Topological phase transition on the ruby lattice with Rashba spin-orbit coupling and an exchange field

We investigate the topological phases in a ruby lattice when considering the effects of the intrinsic spin-orbit coupling, the Rashba spin-orbit coupling and an exchange field. The combination of the Rashba coupling and the exchange field leads to the quantum anomalous Hall effect characterized by a nonzero Chern number. We show that the variation of the exchange field drives interesting topological phase transitions between different topological insulating phases, including the quantum spin Hall insulator with spin Chern number Cs = & PLUSMN;1, the quantum anomalous Hall insulator with Chern number C = & PLUSMN;1 and C = & PLUSMN;2. Particularly, the quantum anomalous Hall phases with high Chern numbers C = -4 and C = 6 can be realized by tuning the strength of the exchange field. Each phase transition is accompanied by closing of the bulk gap. Furthermore, we find a new topological phase which exhibits the electronic characteristics of both the quantum spin Hall effect and the quantum anomalous Hall effect. The band structures of the edge states confirm the classification of various topological gapped phases.