Ultrafast exciton relaxation in monolayer transition metal dichalcogenides

We examine a mechanism by which excitons undergo ultrafast relaxation in common monolayer transition metal dichalcogenides. It is shown that at densities $\approx$ 1$\times$ 10$^{11}$ cm$^{-2}$ and temperatures $ \le 60$ K, excitons in well known monolayers (MoS$_2$, MoSe$_2$, WS$_2$ and WSe$_2$) exist as point-like structureless electron-hole quasi-particles. We evaluate the average rate of exciton energy relaxation due to acoustic phonons via the deformation potential and the piezoelectric coupling mechanisms and examine the effect of spreading of the excitonic wavefunction into the region perpendicular to the monolayer plane. Our results show that the exciton relaxation rate is enhanced with increase in the exciton temperature, while it is decreased with increase in the lattice temperature. Good agreements with available experimental data are obtained when the calculations are extrapolated to room temperatures. A unified approach taking into account the deformation potential and piezoelectric coupling mechanisms shows that exciton relaxation induced by phonons is as significant as defect assisted scattering and trapping of excitons by surface states in monolayer transition metal dichalcogenides.