Topological phase transition in a graphene system with a coexistence of Coulomb interaction, staggered potential, and intrinsic spin-orbit coupling

Abstract

Using a mean-field approximation of the Hubbard model, we investigate the topological phase transition of the graphene system with an intrinsic spin-orbit coupling undergoing a coexistence of a Coulomb interaction and a staggered potential. We find that in an infinite system the antiferromagnetic phase can be classified into four types according to their topological properties: Two of them belong to the normal band-insulator phase, the third type is the quantum spin Hall insulator phase, although the inversion symmetry and the time-reversal symmetry are broken, and the fourth is the spin-polarized quantum Hall insulator phase, a different state of matter possessing Chern number 1 and spin Chern numbers $\frac{1}{2}$, which emerges due to the interplay between the Coulomb repulsion and the breaking of the sublattice symmetry. In addition, the number of edge states in a zigzag graphene ribbon whose parameters belong to one of these types confirms the validity of the analysis of the four phases. All the results obtained from a simplified toy model agree with those acquired from the self-consistent calculation. This indicates that the proposed toy model can exactly and analytically provide the essential information on the phase transition process of such graphene systems.