Effects of Uniaxial Strain on the Electronic Structure of Transition-Metal Dichalcogenides (TMD)*

Using first-principles calculations, we investigate the effects of uniaxial strain on the electronic structure of monolayer MX₂ transition-metal dichalcogenide (TMD) semiconductors with M= (Mo, W) and X= (S, Se, Te). Under equilibrium conditions, the fundamental gaps are direct at K-K with the indirect gap K-Q being slightly higher for some of the compounds. Under uniaxial strain, along the zig-zag or armchair directions, the perfect hexagonal symmetry is broken, and the honeycomb Brillouin zone becomes distorted, leading to shifts in the maxima of the valence band and minima in the conduction band at K, Γ, and Q high-symmetry points. In the range of 0-5% uniaxial tensile strain, the TMDs remain direct band-gap semiconductors, while the difference between the indirect and direct gap increases with tensile strain. We also observe that the valence-band and conduction-band edges are slightly displaced from the K point for strain greater than 2%, changing the degeneracy of the electron and hole valleys, and likely affecting transport and optical properties. Our study emphasizes the effects of spin-orbit coupling and the use of hybrid functionals to correctly predict fundamental band gaps, the splitting of valence-band maximum, and the results of breaking the symmetry under uniaxial strain in TMDs.