Effects of uniaxial strain on monolayer transition-metal dichalcogenides revisited

Abstract

Using hybrid density functional calculations including spin-orbit coupling, we compute the strain evolution of the band structure of monolayer 1H-phase transition-metal dichalcogenides, MX$_2$ (M= Mo, W; X= S, Se, Te), emphasizing an accurate reproduction of the quasiparticle band gap (as opposed to the excitonic optical gap). We show that tensile uniaxial strain applied along either the armchair or zigzag directions leads to a pronounced reduction of the fundamental gap, with the conduction-band edge generally exhibiting the stronger strain response. Both the conduction-band electron valleys (CBM) and the valence-band hole valleys (VBM) remain degenerate under uniaxial strain, while simultaneously drifting away from the high-symmetry $K$ point under strain ("valley drift"), such that the band extrema occur at nearby off-symmetry wave vectors. A minimal tight-binding model rationalizes the valley drift and the unequal electron- and hole-valley drift rates in the presence of strain, leading to indirect band gaps. In particular, for MoS$_2$ the indirectness increases with tensile strain, providing a natural explanation for the experimentally observed decrease in photoluminescence intensity under uniaxial deformation. These results provide quantitative guidance for tailoring band structures for optoelectronic and quantum-defect applications.