Stability of direct band gap under mechanical strains for monolayer MoS2, MoSe2, WS2 and WSe2

Single layer transition-metal dichalcogenides materials (MoS2, MoSe2, WS2 and WSe2) are investigated using the first-principles method with the emphasis on their responses to mechanical strains. All these materials display the direct band gap under a certain range of strains from compressive to tensile (stable range). We have found that this stable range is different for these materials. Through studying on their mechanical properties again using the first-principles approach, it is unveiled that this stable strain range is determined by the Young's modulus. More analysis on strains induced electronic band gap properties have also been conducted.