Spin-orbit modifications and splittings of deep surface states on clean Au(111)

We compare the electronic structure of the unreconstructed Au(111) 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 $E_F$. The existence and spin-orbit splitting of these deeper states should be experimentally detectable by angle-resolved photoelectron spectroscopy