Linear and nonlinear optical response based on the GW-Bethe-Salpeter and Kadanoff-Baym approaches for two-dimensional layered semiconductor materials

The family of 2D layered semiconductors, including transition metal chalcogenides (TMCs) of the form MX (M=Ga, In; X=S, Se, Te) exhibit 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, resulting in non-zero off-diagonal elements of the χ^(2n′) tensor, n′being a positive integer, for arbitrary thickness of the materials. We perform first-principles many-body calculations of band structures and linear and nonlinear optical responses of monolayer (ML) 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 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 observe the general trend that the lowest-energy excitons are dark in 2D ML TMCs whereas they are bright or mixed bright-dark in 3D bulk TMCs, which we attribute to the difference between spatially dependent screening in 2D and constant screening in 3D. In particular, we derive general formulas for the nonlinear optical response based on exciton states in semiconductor materials. We find anti-bound excitons in ML GaS, which we attribute to dominant exciton exchange interaction. 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 SHG and third harmonic generation (THG), but also in general for χ^(n) nonlinear response with n > 3, giving rise to high harmonic generation (HHG) in 2D semiconductor materials. We achieve good to excellent agreement with experimental measurements of linear exciton spectra and nonlinear coefficients for ML and bulk GaS, GaSe, and GaTe for χ^(n) , n = 2 and n = 3. We predict the nonlinear response of InTe and AlTe for 2 < n < 7. The HHG regime has so far been rarely considered, both theoretically and experimentally. We predict high values of SHG, THG, and HHG for the TMC family of materials for 2 ≤n ≤7, which is in agreement with similar trends in transition metal dichalcogenides.