Abstract
We elucidate how the free-electron-like energy dispersion of the L-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 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 the 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.
Highlights
Introduction cri ptThe spin-orbit (SO) splitting of surface bands was first observed for the L-gap surface state on clean Au(111) surfaces by angle-resolved photoemission spectroscopy (ARPES)[1]
The experimental lattice constant of Au is a = 4.08 Å, whereas we obtained via total-energy minimization a = 4.04 Å and 4.15 Å for local density approximation (LDA) and generalized gradient approximation (GGA), respectively, where the calculation was made by using a bulk FLAPW code included in the embedded Green’s function (EGF) program
MeV underestimated if a is set to the GGA value and by ∼100 meV overestimated if a is chosen as the LDA one
Summary
The spin-orbit (SO) splitting of surface bands was first observed for the L-gap surface state on clean Au(111) surfaces by angle-resolved photoemission spectroscopy (ARPES). Reconstructed Au(111) surface to reveal the full band structure of the L-gap surface state For this purpose we use a computational method [13, 26] that combines the embedded Green’s function (EGF) theory of Inglesfield [27, 28] and the full-potential linearized augmented plane-wave (LAPW) method [29]. It will be shown that mini band gaps formed at the crossings of the primary and replica surface bands depend on the amplitude of the SL potential and on mutual spin orientations of the two crossing bands This indicates that, for clean or adsorbed surfaces having a large unit cell, one may obtain information on the spin direction of spin-polarized surface bands by measuring band-gap sizes via non-spin resolved experimental techniques such as spin-integrated ARPES and STM
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