Strain Magnitude and Direction Effect on the Energy Band Structure of Hexagonal and Orthorhombic Monolayer MoS$_2$

We report changes of the band structure of hexagonal and orthorhombic cells of the monolayer molybdenum disulfide (MoS
₂
) subject to various magnitudes and directions of the mechanical strains based on the first principle method. The conduction band minimum (CBM) of this two-dimensional (2-D) material has been calculated to establish the relation with both the magnitude and direction of the strains. It is found that the CBM at Γ point of the hexagonal cell decreases in a slight concave shape for the tensile strain, and a convex shape for the compressive strain. For the orthorhombic cell, we demonstrate that the effect is almost independent on the direction of the applied tensile strain. However, there is a strong directional dependence for compressive strain.