Strain tunable electron-hole excitation and second-harmonic generation in MoS₂ monolayer

Monolayer MoS₂ shows contradictory second-harmonic generation (SHG) signatures in the high-energy region, with experiments reporting either single- or double-peak structures. Here, we systematically compute strain-dependent SHG spectra using a first-principles real-time approach based on the GW-BSE formalism to include excitonic effects. Without strain, a single SHG peak aligns with the absorption peak, arising from nearly degenerate excitons around Γ-centered ring transitions and trigonally warped bands near K/K^'. Tensile strain splits these excitons, producing a double-peak structure, whose broadening and maintained intensity are explained by increased joint density of states from band nesting and enhanced exciton-exciton coupling. In contrast, compressive strain preserves the single-peak feature. Strong compression even reduces SHG intensity due to suppressed trigonal warping, modified exciton character, and weakened coupling. Our results attribute the experimental discrepancies to substrate-induced residual tensile strain and demonstrate how strain can selectively control nonlinear optical responses in two-dimensional materials.