Nonlinear spectroscopy of excitonic states in transition metal dichalcogenides

Second-harmonic generation (SHG) is a well-known nonlinear spectroscopy method to probe electronic structure, specifically, in transition metal dichalcogenide (TMDC) monolayers. This work investigates the nonlinear dynamics of a strongly excited TMDC monolayer by solving the time evolution equations for the density matrix. It is shown that the presence of excitons qualitatively changes the nonlinear dynamics leading, in particular, to a huge enhancement of the nonlinear signal as a function of the dielectric environment. It is also shown that the SHG polarization angular diagram and its dependence on the driving strength are very sensitive to the type of exciton state. This sensitivity suggests that SHG spectroscopy is a convenient tool for analyzing the fine structure of excitonic states.