The key role of non-local screening in the environment-insensitive exciton fine structures of transition-metal dichalcogenide monolayers

In this work, we present a comprehensive theoretical and computational investigation of exciton fine structures of WSe$_2$-monolayers, one of the best known two-dimensional (2D) transition-metal dichalcogenides (TMD's), in various dielectric-layer environments by solving the first-principles-based Bethe-Salpeter equation. While the physical and electronic properties of atomically thin nano-materials are normally sensitive to the variation of surrounding environment, our studies reveal that the influence of dielectric environment on the exciton fine structures of TMD-ML's is surprisingly limited. We point out that the non-locality of Coulomb screening plays a key role to suppress the factor of dielectric environment and drastically shrink the fine structure splittings between bright exciton (BX) states and various dark exciton (DX) states of TMD-ML's. The intriguing non-locality of screening in 2D materials can be manifested by the measurable {\it non-linear} correlation between the BX-DX splittings and exciton binding energies with varying the surrounding dielectric environments. The revealed environment-insensitive exciton fine structures of TMD-ML's suggest the robustness of prospective dark-exciton-based opto-electronics against the inevitable variation of inhomogeneous dielectric environment.