The surface spin states for bismuth thin films are investigated using an $s{p}^3$ tight-binding model. The model explains most experimental observations using angle-resolved photoemission spectroscopy, including the Fermi surface, the band structure with Rashba spin splitting, and the quantum confinement in the energy band gap of the surface states. A large out-of-plane spin component also appears. The surface states penetrate inside the film to within approximately a few bilayers near the Brillouin-zone center, whereas they reach the center of the film near the Brillouin-zone boundary.

• Received 29 June 2015
• Revised 20 October 2015

DOI:https://doi.org/10.1103/PhysRevB.93.041301