Strong Substrate Strain Effects in Multilayered WS Revealed by High-Pressure Optical Measurements.

The optical properties of two-dimensional materials can be effectively tuned by strain induced from a deformable substrate. In the present work we combine first-principles calculations based on density functional theory and the effective Bethe-Salpeter equation with high-pressure optical measurements to thoroughly describe the effect of strain and dielectric environment onto the electronic band structure and optical properties of a few-layered transition-metal dichalcogenide. Our results show that WS remains fully adhered to the substrate at least up to a -0.6% in-plane compressive strain for a wide range of substrate materials. We provide a useful model to describe effect of strain on the optical gap energy. The corresponding experimentally determined out-of-plane and in-plane stress gauge factors for WS monolayers are -8 and 24 meV/GPa, respectively. The exceptionally large in-plane gauge factor confirms transition metal dichalcogenides as very promising candidates for flexible functionalities. Finally, we discuss the pressure evolution of an optical transition closely lying to the A exciton for bulk WS as well as the direct-to-indirect transition of the monolayer upon compression.