  The surface spin states for bismuth thin films were investigated using an
$sp^3$ tight-binding model. The model explains the 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.
