We present a comprehensive theoretical investigation of the excitonic properties of uniaxially strained transition-metal dichalcogenide monolayers (TMD-MLs) by solving the Bethe-Salpeter equation (BSE) in the Wannier tight-binding scheme established on the base of first-principles. The presence of a uniaxial strain in a ${\mathrm{MoS}}_2$-ML is shown to impact most the spin-forbidden exciton states, i.e., gray exciton (GX) and dark exciton (DX) states. As a consequence of strain-induced valley drift and electron-hole exchange interaction, imposing a uniaxial strain onto a ${\mathrm{MoS}}_2$-ML dramatically reshapes the band dispersion of DX from a parabola to a Mexican-hat-like profile, accompanying with unusual sign-reversal of the exciton effective mass and slight strain-activated brightness. Contrarily, the band dispersion of spin-forbidden GX yet remains parabolic but is characterized by a drastically reduced effective mass by an imposed strain. The first-principles-based studies further predict the strain-induced diversification of the exciton diffusivities, transition dipoles, and angle-resolved optical patterns of bright excitons, GXs, and DXs in uniaxially strained TMD-MLs, suggesting the feasibility of spatially resolving spin-allowed and -forbidden excitons in exciton transport and optical spectroscopy experiments.

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• Bethe-Salpeter equation
• Excitons
• First-principles calculations
• Strain
• Transition metal dichalcogenides
• Density functional theory