Electronic structure of the tungsten (001) surface

A self-consistent scalar-relativistic version of the linear-augmented-plane-wave (LAPW) method has been applied to calculate the electronic structure of an unrelaxed seven-layer W(001) slab. The results have been extended to a thicker (19-layer) film and the fully relativistic limit by means of a nonorthogonal-tight-binding (NTB) scheme that combines parameters derived from accurate NTB fits (∼6 mRy) to the bulk LAPW band structure and the seven-layer slab results. The latter fit incorporates bulk NTB parameters for the interior, relaxed bulk parameters near the surface, and additional crystal-field terms in the two outermost layers. The present scalar-relativistic LAPW and NTB surface-state bands are in good qualitative agreement with those calculated previously by Posternak et al. It is shown that the effects of spin-orbit coupling produce significant changes in the surface-state dispersion for ${\overrightarrow{\mathrm{k}}}_{\parallel }$ along the $\overline{\Sigma }$ or [11] direction of the surface Brillouin zone. These changes reduce the serious discrepancy that exists between the calculated scalar-relativistic surface-state dispersion curves along $\overline{\Sigma }$ and those determined in recent high-resolution angle-resolved—photoemission-spectroscopy studies.