Elastic Anisotropy and Optic Isotropy in Black Phosphorene/Transition-Metal Trisulfide van der Waals Heterostructures

Anisotropic two-dimensional materials with direction-dependent mechanical and optical properties have attracted significant attention in recent years. In this work, based on density functional theory calculations, unexpected elastic anisotropy and optical isotropy in van der Waals (vdW) heterostructures have been theoretically proposed by assembling the well-known anisotropic black phosphorene (BP) and transition-metal trisulfides MS₃ (M = Ti, Hf) together. It is interesting to see that the BP/MS₃ vdW heterostructures show anisotropic flexibility in different directions according to the elastic constants, Young's modulus, and Poisson's ratio. We have further unraveled their physical origin of the type-II band structure nature with their conduction band minimum and valence band maximum separated in different layers. In particular, our results on the optical response functions including the excitonic effects of the BP/MS₃ vdW heterostructures suggest their unexpected optical isotropies together with the enhancements of the solar energy conversion efficiency.