Spatiotemporal dynamics of free and bound excitons in CVD-grown MoS$_2$ monolayer

We study photoluminescence (PL) spectra and exciton dynamics of MoS$_2$ monolayer (ML) grown by the chemical vapor deposition technique. In addition to the usual direct A-exciton line we observe a low-energy line of bound excitons dominating the PL spectra at low temperatures. This line shows unusually strong redshift with increase in the temperature and submicrosecond time dynamics suggesting indirect nature of the corresponding transition. By monitoring temporal dynamics of exciton PL distribution in the ML plane we observe diffusive transport of A-excitons and measure the diffusion coefficient up to $40$~cm$^2$/s at elevated excitation powers. The bound exciton spatial distribution spreads over tens of microns in $\sim 1$ $\mu$s. However this spread is subdiffusive, characterized by a significant slowing down with time. The experimental findings are interpreted as a result of the interplay between the diffusion and Auger recombination of excitons.