Theory of second-order excitonic nonlinearities in transition metal dichalcogenides

Single layers of transition metal dichalcogenides exhibit tightly bound excitons with large oscillator strength making them to promising materials for future optoelectronic applications. Despite that the linear response of these ultrathin materials is extensively studied, a profound understanding of the excitonic second-order nonlinear optical response, including trigonal warping and Berry curvature effects, is lacking so far. To bridge this gap, in this paper we report a microscopic model for the second-order nonlinear susceptibility tensor of these materials. Based on a kp description of the underlying many-particle Hamiltonian we are able to address excitonic features as well as trigonal warping effects, spin-valley coupling, and also Berry curvature to the susceptibility tensor. We present explicit calculation of the latter for the exemplary materials MoS2 and WS2 on silicon substrate and encapsulated in hBN. For instance we predict resonant susceptibility for second-harmonic generation 0.5-1.3 nm/V and double-resonant susceptibility 10-30 nm/V for the difference and sum-frequency generation processes. Our results are in good agreement with available experimental findings in the literature.