  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.
