Doping-Induced Brightening of Dark Excitons and Trions in a WSe$_2$ Monolayer
Optically dark excitonic states play a critical role in the valleytronic, electronic, and optical properties of monolayer semiconducting transition metal dichalcogenides. Here, we investigate how electrostatic doping affects the in-plane magnetic-field-induced activation of dark excitonic complexes in a gated WSe$_2$ monolayer. By continuously tuning the carrier density via gate voltage, we access $n$-type, charge-neutral, and $p$-type regimes and track the corresponding brightening dynamics. We find that the brightening rates of the dark negative trion ($T^{D-}$), dark neutral exciton ($X^{D}$), and dark positive trion ($T^{D+}$) exhibit a strong and nontrivial dependence on doping. In particular, the pronounced asymmetry in the brightening behaviour of the neutral $X^{D}$ complex and the charged $T^{D-}$ and $T^{D+}$ trions reveals distinct underlying carrier interactions, which we describe using a rate-equation model for their steady-state populations. These findings highlight the key role of dark excitonic complexes in governing the optical response and carrier dynamics of doped S-TMD monolayers.