Exciton formation assisted by longitudinal optical phonons in monolayer transition metal dichalcogenides

We examine a mechanism by which excitons are generated via the LO (longitudinal optical) phonon-assisted scattering process after optical excitation of monolayer transition metal dichalcogenides. The exciton formation time is computed as a function of the exciton center-of-mass wavevector, electron and hole temperatures, and carrier densities for known values of the Fr\"ohlich coupling constant, LO phonon energy, lattice temperature, and the exciton binding energy in layered structures. For the monolayer MoS$_2$, we obtain ultrafast exciton formation times on the sub-picosecond time scale at charge densities of 5 $\times$ 10$^{11}$ cm$^{-2}$ and carrier temperatures less than 300 K, in good agreement with recent experimental findings ($\approx$ 0.3 ps). While excitons are dominantly created at zero center-of-mass wavevectors at low charge carrier temperatures ($\approx$ 30 K), the exciton formation time is most rapid at non-zero wavevectors at higher temperatures ($\ge $ 120 K) of charge carriers. The results show the inverse square-law dependence of the exciton formation times on the carrier density, consistent with a square-law dependence of photoluminescence on the excitation density. Our results show that excitons are formed more rapidly in exemplary monolayer selenide-based dichalcogenides (MoSe$_2$ and WSe$_2$) than sulphide-based dichalcogenides (MoS$_2$ and WS$_2$).