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

TL;DR

This paper develops a simplified three-band tight-binding model for monolayer transition metal dichalcogenides, accurately capturing low-energy electronic properties and spin-orbit effects across the entire Brillouin zone.

Contribution

It introduces a minimal three-orbital tight-binding model fitted to first-principles data, effectively describing the electronic structure of $MX_2$ monolayers including spin-orbit interactions.

Findings

Accurately reproduces band-edge properties at $ ext{K}$ points

Captures Berry curvature and valley-dependent spin splitting

Efficiently models entire Brillouin zone with third-nearest-neighbor hoppings

Abstract

We present a three-band tight-binding (TB) model for describing the low-energy physics in monolayers of group-VIB transition metal dichalcogenides $MX_2$ ($M$=Mo, W; $X$=S, Se, Te). As the conduction and valence band edges are predominantly contributed by the $d_{z^{2}}$, $d_{xy}$, and $d_{x^{2}-y^{2}}$ 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 $MX_2$ monolayers. The TB model involving only the nearest-neighbor $M$-$M$ hoppings is sufficient to capture the band-edge properties in the $\pm K$ 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 Mo$X_{2}$ and W$X_{2}$. 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 $MX_2$ monolayers, and its simplicity can be particularly useful in the study of many-body physics and physics of edge states.