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A tight-binding model of bcc tungsten that includes spin-orbit coupling isdeveloped and applied to the surface states of (110) tungsten thin films. Themodel describes accurately the anisotropic Dirac cone-like dispersion andRashba-like spin polarization of the surface states, including the crucialeffect of the relaxation of the surface atomic layer of the tungsten towardsthe bulk. It is shown that the surface relaxation affects the tungsten surfacestates because it results in increased overlaps between atomic orbitals of thesurface atomic layer and nearby layers whereas electric fields that are due tocharge transfer between the tungsten and the vacuum near the surface or betweenthe bulk and surface layers do not significantly affect the Rashba-Diracsurface states. It is found that hybridization with bulk modes has differingstrengths for thin film surface states belonging to the upper and lowerRashba-Dirac cones and results in $reversal$ of the directions of travel ofspin $\uparrow$ and $\downarrow$ electrons in most of the upper Rashba-Diraccone relative to those expected from phenomenology. It is also shown thatintrasite (not intersite) matrix elements of the spin-orbit Hamiltonian areprimarily responsible for the formation of the Rashba-Dirac cones, and theirspin polarization. This finding should be considered when modeling topologicalinsulators, the spin Hall effect and related phenomena.

Rashba-Dirac cones at the tungsten surface: Insights from a tight-binding model and thin film subband structure