We introduce a solvable four-band model to study electron energy levels in disordered transition metal dichalcogenides. Electron states in the pristine monolayer are described by a k Hamiltonian. Point defects are assumed to be randomly distributed on a regular lattice. The interaction of electrons with the defects is accounted for by a separable pseudopotential, thus yielding a solvable model suitable for long- and short-range interactions. The coherent potential approximation is used to obtain the configurationally averaged density of states. We compare to models of disorder, namely, binary disorder and Anderson disorder. Importantly, both disorder models yield consistent outcomes, demonstrating that an increase in disorder strength results in a narrowing of the energy gap. Remarkably, CPA with binary disorder provides results that are in very good agreement with available density functional theory and experimental data for the optical gap in the monolayer alloy Mo₁-ₗWₗS₂. Moreover, it entails less computational effort than density functional theory calculations.
Ruano et al. (Mon,) studied this question.