Spin-orbit modifications and splittings of deep surface states on clean Au(1 1 1)

We compare the electronic structure of the unreconstructed Au(1 1 1) surface calculated within density functional theory by means of plane waves and fully-relativistic ultrasoft pseudo-potentials (US-PPs) on one hand, and scalar relativistic US-PPs on the other hand, where spin-orbit is not included. Several surface states are identified and discussed, in particular their character and spin polarization caused by the spin-orbit interaction. Besides the well known splitting of the L-gap shallow surface state near the Fermi energy, the spin-orbit interaction generates, modifies, and splits many other deep surface states in the range 1-10 eV below EF. The existence and spin-orbit splitting of these deeper states should be experimentally detectable by angle-resolved photoelectron spectroscopy.