A first-principles study on the Rashba effect in surface systems

The Rashba effect in several surface systems, Au(111), Au(110), Ag(111), Sb(111) and Si(111)-Bi, is studied by means of first-principles relativistic density-functional calculations. The importance of the asymmetric behavior around the surface atom is emphasized as a crucial factor to determine the magnitude of Rashba spin splitting in addition to the size of the spin-orbit coupling. The Rashba effect at the Brillouin-zone boundary is generally described with time-reversal symmetry. Distinctive features in the spin splitting and spin direction for a two-dimensional hexagonal system are discussed with the use of symmetry in the double group of k.