Study of Spin-Orbit Coupling Effect on Bismuth (111) Bilayer

Band inversion process in Bi(111) bilayer is studied using many-orbital tight-binding model, supported by the density-functional theory calculations, with a controllable spin-orbit coupling constant in tight-binding model. This effect is important in order to verify a topological nature of this material. We show that after closing of the energy gap leading to crossing of the valence and conduction bands, the second band inversion occurs within a valence band. We analyze orbital composition and spin textures of bands within different regimes. Around a Γ point, all spins align in one direction before the first band inversion. Moreover, a change of signs for some spin components after a band inversion is noticed. After the second band inversion, a significant change of orbital contribution of the top of the valence band is observed.