Exciton Enhanced\nNonlinear Optical Responses in Monolayer\nh‑BN and MoS<sub>2</sub>: Insight from First-Principles Exciton-State\nCoupling Formalism and Calculations

Excitons are vital in the photophysics of materials,\nespecially\nin low-dimensional systems. The conceptual and quantitative understanding\nof excitonic effects in nonlinear optical (NLO) processes is more\nchallenging compared to linear ones. Here, we present an ab initio\napproach to second-order NLO responses, incorporating excitonic effects,\nthat employs an exciton-state coupling formalism and allows for a\ndetailed analysis of the role of individual excitonic states. Taking\nmonolayer h-BN and MoS<sub>2</sub> as two prototype 2D materials,\nwe calculate their second harmonic generation (SHG) susceptibility\nand shift current conductivity tensor. We find strong excitonic enhancement\nin the NLO responses requires that the resonant excitons are not only\noptically bright themselves but also able to couple strongly to other\nbright excitons. Our results explain the occurrence of two strong\npeaks in the SHG of monolayer h-BN and why the A and B excitons of\nMoS<sub>2</sub> unexpectedly exhibit minimal excitonic enhancement\nin both SHG and shift current generation.