Identifying optical signatures of momentum-dark excitons in transition metal dichalcogenide monolayers

Transition metal dichalcogenide (TMD) monolayers (MLs) exhibit rich photoluminescence spectra associated with interband optical transitions of direct-gap semiconductors. Upon absorption of photons, direct excitons with zero center-of-mass momentum are formed by photo-excited electrons in the conduction band and the respective unoccupied states in the valence band of the same valley. Different spin configurations of such momentum-direct excitons as well as their charged counterparts provide a powerful platform for spin-valley and microcavity physics in two-dimensional materials. The corresponding spectral signatures, however, are insufficient to explain the main characteristic peaks observed in the photoluminescence spectra of ML TMDs on the basis of momentum-\textit{direct} excitons alone. Here, we show that the notion of momentum-\textit{indirect} excitons is important for the understanding of the versatile photoluminescence features. Taking into account phonon-assisted radiative recombination pathways for electrons and holes from dissimilar valleys, we interpret unidentified peaks in the emission spectra as acoustic and optical phonon sidebands of momentum-dark excitons. Our approach will facilitate the interpretation of optical, valley and spin phenomena in TMDs arising from bright and dark exciton manifolds.