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The coherent third-order nonlinear response of monolayer transition-metaldichalcogenide (TMD) semiconductors, such as MoSe$_2$ is dominated by thenonlinear exciton response, as well as biexciton and trion resonances. The factthat these resonances may be spectrally close together makes identification ofthe signatures, for example in differential transmission (DT), challenging.Instead of focusing on explaining a given set of experimental data, asystematic study aimed at elucidating the roles of intravalley and intervalleyelectron-hole (e-h) exchange on the DT spectra is presented. Previous workshave shown that the e-h exchange introduces a linear leading-order term in theexciton dispersion. Based on a generalized Lippmann-Schwinger equation, we showthat the presence of this linear dispersion term can reduce the biexcitonbinding energy to zero, contrary to the conventional situation of quadraticdispersion where an arbitrarily weak (well-behaved) attractive interactionalways supports bound state(s). The effects of spin-scattering and thespin-orbit interaction caused by e-h exchange is also clarified, and the DTlineshape at the exciton and trion resonance are studied as a function of e-hexchange strength. In particular, as the exciton lineshape is determined by theinterplay of linear exciton susceptibility and the bound-state two-excitonresonance in the T-matrix, the lineshape at the trion is similarly determinedby the interplay of the linear trion susceptibility and the bound-stateexciton-trion resonance in the T-matrix.

Effect of intravalley and intervalley electron-hole exchange on the nonlinear optical response of monolayer MoSe$_2$