Long-lived populations of momentum- and spin-indirect excitons in monolayer WSe₂

In monolayer WSe₂, the ground-state exciton is dark (D exciton, spin-indirect), and the valley degeneracy allows low-energy dark momentum-indirect excitons (X_K exciton) to form. Interactions between the dark excitons and the optically accessible bright exciton (X) are likely to determine the optical properties of X at high power and to limit the maximum achievable exciton densities. However, so far, little is known about these interactions. Here, we show long-lived dense populations of the X_K and the D excitons by performing time-resolved photoluminescence spectroscopy using a streak camera. Our results uncover an efficient inter-state conversion between X to D excitons through the spin-flip process. Surprisingly, we also observe a prominent conversion between the dark excitons mediated by the exchange interaction (D + D ↔ X_K + X_K). This interaction behaves superlinearly to the exciton densities and responsible for the population of the X_K exciton at high densities. Moreover, the long-lived X_K exciton can induce a persistent redshift of X exciton, revealing non-trivial exciton-exciton interactions. Our results clarify the interactions between bright and dark excitons, and further envision the Bose-Einstein condensation of dark excitons.