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In this work, we present a comprehensive theoretical and computationalinvestigation of exciton fine structures of WSe$_2$-monolayers, one of the bestknown two-dimensional (2D) transition-metal dichalcogenides (TMD's), in variousdielectric-layer environments by solving the first-principles-basedBethe-Salpeter equation. While the physical and electronic properties ofatomically thin nano-materials are normally sensitive to the variation ofsurrounding environment, our studies reveal that the influence of dielectricenvironment 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 tosuppress the factor of dielectric environment and drastically shrink the finestructure splittings between bright exciton (BX) states and various darkexciton (DX) states of TMD-ML's. The intriguing non-locality of screening in 2Dmaterials can be manifested by the measurable {\it non-linear} correlationbetween the BX-DX splittings and exciton binding energies with varying thesurrounding dielectric environments. The revealed environment-insensitiveexciton fine structures of TMD-ML's suggest the robustness of prospectivedark-exciton-based opto-electronics against the inevitable variation ofinhomogeneous dielectric environment.

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