Density Saturation and Autocorrelation Characteristics of Interlayer Exciton Ensembles in MoSe$_2$/WSe$_2$ Heterostructures
We investigate interlayer excitons in MoSe$_2$/WSe$_2$ heterostructures using time-resolved photoluminescence and second-order autocorrelation measurements across a wide range of excitation powers and bath temperatures. By analyzing the photoluminescence amplitude and lifetime of the interlayer exciton state with the lowest emission energy, we extract a corresponding density-temperature diagram. The extracted exciton density exhibits a saturation at approximately $10^{13}$cm$^{-2}$, consistent with values predicted for a Mott transition of interlayer exciton ensembles in van der Waals heterostructures. Moreover, possible interpretations beyond the Mott transition are discussed. We further test whether the density limit is accompanied by a departure from classical photon statistics. The second-order autocorrelation measurements reveal that the photoluminescence maintains an emission characteristic of $g^{(2)}(0) \approx 1$ from low exciton densities up to the maximum reachable density in the investigated exciton ensembles consistent with the lowest-energy exciton ensemble obeying Poissonian statistics.