Linear and nonlinear optical response based on many-body GW-Bethe–Salpeter and Kadanoff–Baym approaches for two-dimensional layered semiconductors

The family of 2D layered semiconductors, including transition metal chalcogenides (TMCs), exhibits exceptional nonlinear optical properties. The energetically most favorable crystal ordering for nonlinear response is the AB layer stacking, which breaks central inversion symmetry for an arbitrary number of layers. We perform first-principles many-body calculations of band structures and linear and nonlinear optical responses of monolayer and bulk TMC crystals based on GW-Bethe-Salpeter and Kadanoff-Baym approaches in and out of equilibrium, respectively, while taking many-body band gap renormalization and excitonic effects into account. We develop a detailed analysis of the linear and nonlinear optical selection rules by means of group and representation theory, showing a strong connection to crystal symmetry and orbital characters of the bands and providing a method to predict the strength of linear and nonlinear response of new materials. We show that by choosing elements with larger mass and by reducing the detuning energy it is possible to increase the nonlinear response not only for χ(2) and χ(3), responsible for second and third harmonics generation, but also in general for χ(n) nonlinear response with n > 3, giving rise to high harmonic generation.