Nonexponential photoluminescence dynamics in an inhomogeneous ensemble of excitons in WSe$_2$ monolayers

The spectral and spatiotemporal dynamics of photoluminescence in monolayers of transition metal dichalcogenide WSe$_2$ obtained by mechanical exfoliation on a Si/SiO$_2$ substrate is studied over a wide range of temperatures and excitation powers. It is shown that the dynamics is nonexponential and, for times t exceeding $\sim50$ ps after the excitation pulse, is described by a dependence of the form $1/(t + t_0)$. Photoluminescence decay is accelerated with a decrease in the temperature and in the energy of emitting states. It is shown that the observed dynamics cannot be described by a bimolecular recombination process, such as exciton–exciton annihilation. A model that describes the nonexponential photoluminescence dynamics by taking into account the spread of radiative recombination times of localized exciton states in a random potential gives good agreement with experimental data.