Directional dependence of band gap modulation via uniaxial strain in MoS2 and TiS3

Strain is widely employed to modulate the band structures of two-dimensional (2D) van der Waals (vdW) materials. Such band engineering with strain applied along different crystallographic directions, however, is less explored. Here, we investigate the band gap modulation of layered chalcogenides, MoS2 and TiS3, and the dependence of their band gaps on the directions of applied strain, using first-principles calculations. The band gap transition in MoS2 is found to reduce in energy linearly as a function of increasing tensile strain, with a weakly directional-dependent gradient, varying by 4.6 meV/% (from -52.7 +/- 0.6 to -57.3 +/- 0.1 meV/%) from the zigzag to armchair directions. Conversely, the band gap in TiS3 decreases with strain applied along the a lattice vector, but increases with strain applied in the perpendicular direction, with a non-linear strain-band gap relationship found between these limits. Analysis of the structure of the materials and character of the band edge states under strain helps explain the origins of the stark differences between MoS2 and TiS3. Our results provide new insights for strain engineering in 2D materials and the use of the direction of applied strain as another degree of freedom.