Figure 4. Ab initio calculated band structures for WS₂ ultrathin films.

(a–d): without spin-orbit coupling; (e–h): with spin-orbit coupling. The valence band splittings at K point are nearly constants, around 0.43 eV for mono-,bi-, tri, and quad-layers; (i) Electron density map for one valence band Bloch state at K point in WS₂ bilayer (indicated by the dashed arrow in (f)). The wavefunction is fully spin polarized in the down state and almost fully localized in the bottom layer. The other degenerate state at the same K point can be obtained by a spatial inversion plus a time reversal operation.