Abstract
We utilize first-principles calculations within density-functional theory to investigate the possibility of strain engineering in the tuning of the band structure of two-dimensional <TEX>$MoS_2$</TEX>. We find that the band structure of <TEX>$MoS_2$</TEX> monolayers transits from direct to indirect when mechanical strain is applied. In addition, we discuss the change in the band gap energy and the critical stains for the direct-to-indirect transition under various strains such as uniaxial, biaxial, and pure shear. Biaxial strain causes a larger change, and the pure shear stain causes a small change in the electronic band structure of the <TEX>$MoS_2$</TEX> monolayer. We observe that the change in the interaction between molecular orbitals due to the mechanical strain alters the band gap type and energy.
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