Strain dependence of band gaps and exciton energies in pure and mixed transition-metal dichalcogenides

The ability to fabricate 2D device architectures with desired properties, based on stacking of weakly (van der Waals) interacting atomically thin layers, is quickly becoming reality. In order to design ever more complex devices of this type, it is crucial to know the precise strain and composition dependence of the layers' electronic and optical properties. Here, we present a theoretical study of these dependences for monolayers with compositions varying from pure ${MX}_{2}$ to the mixed $MXY$, where $M=\text{Mo}$, W and $X,Y=\text{S}$, Se. We employ both density-functional-theory and GW calculations, as well as values of the exciton binding energies based on a self-consistent treatment of dielectric properties, to obtain the band gaps that correspond to optical or transport measurements; we find reasonable agreement with reported experimental values for the unstrained monolayers. Our predictions for the strain-dependent electronic properties should be a useful guide in the effort to design heterostructures composed of these layers on various substrates.