Spin-dependent band-gap formation for theL-gap surface state on the(22×3)reconstructed Au(111) surface

We elucidate how the free-electron-like energy dispersion of theL-gap surface state on a Au(111)-(1 × 1) surface is modified by the experimentally observed uniaxial reconstruction of the topmost atomic layer. For this purpose, we perform a first-principles embedded Green's function calculation for the(22×3)reconstructed semi-infinite Au(111) surface. The obtained band structure unfolded into the surface Brillouin zone of the (1 × 1) surface can be understood in terms of two spin-split parabolic bands centered at theΓ¯point, their umklapp-induced replicas centered at reciprocal lattice vectors of the superlattice (SL) with much weaker intensities, and mini band gaps at the crossing of two of them. More importantly, it is revealed that the band-gap size depends not only on the amplitude of the SL potential but also on mutual spin orientations of two crossing bands. Furthermore, we demonstrate that the band-gap size and the charge density distribution of the surface states are closely correlated with spatial profile of the SL potential.