  We characterize the electronic structure and elasticity of monolayer
transition-metal dichalcogenides MX2 (M=Mo, W, Sn, Hf and X=S, Se, Te) with 2H
and 1T structures using fully relativistic first principles calculations based
on density functional theory. We focus on the role of strain on the band
structure and band alignment across the series 2D materials. We find that
strain has a significant effect on the band gap; a biaxial strain of 1%
decreases the band gap in the 2H structures, by as a much 0.2 eV in MoS2 and
WS2, while increasing it for the 1T materials. These results indicate that
strain is a powerful avenue to modulate their properties; for example, strain
enables the formation of, otherwise impossible, broken gap heterostructures
within the 2H class. These calculations provide insight and quantitative
information for the rational development of heterostructures based on these
class of materials accounting for the effect of strain.
