A simple tight-binding model of spin–orbit splitting of sp-derived surface states

In crystals with inversion symmetry, splitting of states due to the spin–orbit interaction is not allowed. At the surface, however, the symmetry is broken, and spin–orbit splitting becomes possible. Spin–orbit splitting has been observed experimentally for the sp-derived surface state on Au(111) [S. LaShell, B.A. McDougall, E. Jensen, Phys. Rev. Lett. 77 (1996) 3419]. We present a simple tight-binding model, which shows that the spin–orbit splitting can be described within a nearly-free-electron model, and the splitting depends on (1) the spin–orbit splitting of the atomic levels and (2) the surface potential. Furthermore, we show that the splitting of the surface state is unobservable in the surface charge density as probed with scanning tunneling microscopy.