Topological phase transition induced by spin–orbit coupling in bilayer graphene

Abstract

We study the topological phase transition in biased bilayer graphene in the presence of intrinsic and Rashba spin-orbit couplings. The system exhibits a complicated topological phase transition depending on the given parameters. The topological phase transition between these phases is always accompanied by the bulk gap closing and reopening, and can be realized by tuning the bias voltage. The stability of these topological phases are also investigated. We find that the weak (strong) topological insulator phase remains stable under a finite exchange field provided that the effect of intrinsic (Rashba) spin-orbit coupling is dominant, and this also holds for the quantum valley Hall phase if the spatial inversion symmetry breaking overcomes the time-reversal symmetry breaking.