Effect of intravalley and intervalley electron-hole exchange on the nonlinear optical response of monolayer MoSe2

The coherent third-order nonlinear response of monolayer transition-metal dichalcogenide semiconductors, such as ${\mathrm{MoSe}}₂$, is dominated by the nonlinear exciton response, as well as biexciton and trion resonances. The fact that these resonances may be spectrally close together makes identification of the signatures, for example in differential transmission (DT), challenging. Instead of focusing on explaining a given set of experimental data, a systematic study aimed at elucidating the roles of intravalley and intervalley long-range electron-hole $(e\ensuremath{-}\mathrm{h})$ exchange on the DT spectra is presented. Previous works have shown that the $e\ensuremath{-}\mathrm{h}$ long-range exchange introduces a linear leading-order term in the exciton dispersion. Based on a generalized Lippmann-Schwinger equation, we show that the presence of this linear dispersion term can reduce the biexciton binding energy to zero, contrary to the conventional situation of quadratic dispersion where an arbitrarily weak (well-behaved) attractive interaction always supports bound state(s). The effects of spin scattering and the spin-orbit interaction caused by $e\ensuremath{-}\mathrm{h}$ exchange are also clarified, and the DT line shape at the exciton and trion resonance is studied as a function of $e\ensuremath{-}\mathrm{h}$ exchange strength. In particular, as the exciton line shape is determined by the interplay of linear exciton susceptibility and the bound-state two-exciton resonance in the $T$ matrix, the line shape at the trion is similarly determined by the interplay of the linear trion susceptibility and the bound-state exciton-trion resonance in the $T$ matrix.