Spin-orbit effects in the electronic structure of the (001) surface of bcc4dand5dtransition metals

In view of explaining surface-sensitive structures observed in recent field-emission and photoemission experiments, a formalism is developed for the investigation of the electronic structure in the vicinity of the Fermi energy of the (001) surface of bcc $4d$ and $5d$ transition metals. Starting from a three-band model tight-binding fit to a known bulk band structure along $\Gamma H$ that contains spin-orbit effects, the Green's function for an infinite crystal is obtained, and subsequently employed in a Dyson equation for the Green's function of a finite crystal. From the latter function, the local densities of states per monatomic layer for ${\overrightarrow{\mathrm{k}}}_{\parallel }=0\mathrm{}$ are determined. The numerical application of this formalism to W(001) and Mo(001) reveals a very pronounced surface resonance in a "relative" band gap just below the Fermi energy and a surface state in an "absolute" gap somewhat further below. The resonance provides an explanation for a surface-sensitive peak below the Fermi level that has been found in a large number of field and photoemission energy distribution measurements. For the surface state, however, there is no clear experimental evidence. For Nb(001) and, in particular, Ta(001), analogous features are predicted above the Fermi level.