Relativistic energy bands of (010) tungsten thin films

We have made the first complete thin-film energy-band calculation including the spin-orbit interaction. Except for the inclusion of spin-orbit parameters, the method used is identical to the parametrization scheme we have previously applied to several $3d$ transition metals. Two of the three surface features observed in tungsten(001) photoemission are found near Γ as well as many other surface states throughout the two-dimensional Brillouin zone. Spin-orbit induced surface states are found in Γ, X̄, and M̄ gaps and an unexpected spin-orbit splitting of the degenerate surface states on opposite sides of the film is found and explained.