Spin-splitting band dispersions of the heavy elements on Si(111)-(1×1) surface

We have carried out the first-principles fully relativistic electronic structure calculations for the surfaces, R/Si(111) (R = Pb and Bi). The band dispersions of the surface states in the bulk band gap shows the large spin splitting, associated with the spin-orbit interaction on the atoms of the overlayer. Besides the usual Rashba effect around the center of the surface Brillouin zone, the vortical spin polarizations were obtained around the M ̄ points. At the K̄, associated with the symmetry, the complete out-of-plane spin polarization was obtained for the surface states.