  Point defects, local strain or impurities can crucially impact the optical
response of atomically thin two-dimensional materials as they offer trapping
potentials for excitons. These trapped excitons appear in photoluminescence
spectra as new resonances below the bright exciton that can even be exploited
for single photon emission. While large progress has been made in
deterministically introducing defects, only little is known about their impact
on the optical fingerprint of 2D materials. Here, based on a microscopic
approach we reveal direct signatures of localized bright excitonic states as
well as indirect phonon-assisted side bands of localized momentum-dark
excitons. The visibility of localized excitons strongly depends on temperature
and disorder potential width. This results in different regimes, where either
the bright or dark localized states are dominant in optical spectra. We trace
back this behavior to an interplay between disorder-induced exciton capture and
intervalley exciton-phonon scattering processes.
