Three-band tight-binding model for monolayers of group-VIB transition metal dichalcogenides

We present a three-band tight-binding (TB) model for describing the low-energy physics in monolayers of group-VIB transition metal dichalcogenides MX₂ (M=Mo, W; X=S, Se, Te). As the conduction- and valence-band edges are predominantly contributed by the d_z², d_xy, and d_x²-y² orbitals of M atoms, the TB model is constructed using these three orbitals based on the symmetries of the monolayers. Parameters of the TB model are fitted from the first-principles energy bands for all MX₂ monolayers. The TB model involving only the nearest-neighbor M-M hoppings is sufficient to capture the band-edge properties in the ±K valleys, including the energy dispersions as well as the Berry curvatures. The TB model involving up to the third-nearest-neighbor M-M hoppings can well reproduce the energy bands in the entire Brillouin zone. Spin-orbit coupling in valence bands is well accounted for by including the on-site spin-orbit interactions of M atoms. The conduction band also exhibits a small valley-dependent spin splitting which has an overall sign difference between MoX₂ and WX₂. We discuss the origins of these corrections to the three-band model. The three-band TB model developed here is efficient to account for low-energy physics in MX₂ monolayers, and its simplicity can be particularly useful in the study of many-body physics and physics of edge states.