  WSe$_2$ monolayers with variable doping are an ideal system to study
two-dimensional excitonic complexes. Here, we find that the strongest
photoluminescence from bright neutral excitons occurs at moderate $p$-doping
levels, owing to a rapid decrease of signal from positive dark trions and a
slow increase of signal from positive bright trions with growing
$p$-concentrations. We explain our observations with a qualitative model, in
which the scattering rate of bright excitons into dark complexes is enhanced by
exciton localization, while the scattering rate into positive bright trions
increases with $p$-doping level.
