First-principles study of spin texture and Fermi lines in Bi(111) multi-layer nanofilm

We have performed a fully relativistic first-principles density functional calculation examining the surface state of bismuth (Bi) (111) multi-layer nanofilm, with up to 20 Bi bilayers, and investigated the Rashba effect and spin texture on the Bi surfaces. We have revealed a giant out-of-plane spin states on the Fermi lines, and the maximum value of the out-of-plane spin component being approximately 40% of the magnitude of the total spin. We have also evaluated the Rashba parameter $\alpha_R \simeq 1.9 {\rm eV}\cdot$\AA using the surface state bands which is buried in the bulk state, at -0.32 eV below the Fermi energy.