Rashba Effect on the Structure of the Bi One-Bilayer Film: Fully Relativistic First-Principles Calculation

Abstract

Using first-principles calculations, we study the spin–orbit interactions and spin textures of a Bi one-bilayer film, which attracts scientific interest because of the topological insulator and so on. The substrate effect is successfully mimicked by applying on electric field in the perpendicular direction of the film, which breaks the inversion symmetry. We study the highest occupied band around the Γ point. Although the vortex of the in-plane spin component is well explained on the basis of the conventional Rashba effect, we find a substantial out-of-plane component which cannot be explained by the conventional Rashba model. This spin texture is similar to that of a multi-bilayer Bi film, which has recently been observed using a spin-resolved angle-resolved photoemission spectroscopy experiment. We also find a spin vortex around the K point although this point has no time-reversal symmetry. We expect that a similar vortex appears in materials having the p 3 m 1 symmetry, whose spin–orbit interactions have recently attracted scientific interest.