Sum-over-exciton-states method for light induced anomalous Hall effects

In low-dimensional semiconductors, low-energy excitations are dominated by excitons, which are strongly correlated electron–hole pairs that govern light–matter interactions. While excitonic effects are known to strongly enhance linear optical responses due to quantum confinement and reduced screening, their roles in nonlinear optical processes are much less understood. In this work, we develop an ab initio sum-over-exciton-states framework for nonlinear optical responses that is directly applicable to real materials. This approach, based on the GW plus Bethe-Salpeter equation results, enables first-principles calculations of nonlinear (second-order and higher) optical coefficients and provides clear insight into the contributions of individual excitons. As a demonstration, we investigate the light induced anomalous Hall effect in monolayer MoS₂ and find that the relative contributions of different excitons differ markedly from those in linear optical responses. We further extend the analysis to other third-order optical processes, showing that our framework offers a general route to understand and predict exciton-mediated nonlinear phenomena in semiconductor systems.