Spin-orbit coupling-induced band inversion and spin Chern insulator phase in plumbene and stanene

Z₂ topology in two-dimensional group IVA materials has been explained by the band orders due to the crystal field splitting at the Γ point in the Brillouin zone, while spin-orbit coupling (SOC) was considered just to open a band gap. By using a multi-orbital tight-binding model, we show that the SOC induces band inversion between the conduction and valence bands at the Γ point in plumbene, which also is the case in stanene when the SOC strength increases. As a result of the band inversion, plumbene becomes a spin Chern insulator with a spin Chern number C_S = 2 and, as the SOC strength increases, stanene undergoes a topological phase transition from a Z₂ topological insulator to a spin Chern insulator with C_S = 2. Under a staggered AB-sublattice potential, plumbene undergoes a phase transition from the spin Chern insulator with C_S = 2 to a Z₂ topological insulator with C_S = 1.