  Using time-resolved optical Kerr rotation, we measure the low temperature
valley dynamics of resident electrons and holes in exfoliated WSe$_2$
monolayers as a systematic function of carrier density. In an effort to
reconcile the many disparate timescales of carrier valley dynamics in monolayer
semiconductors reported to date, we directly compare the doping-dependent
valley relaxation in two electrostatically-gated WSe$_2$ monolayers having
different dielectric environments. In a fully-encapsulated structure
(hBN/WSe$_2$/hBN, where hBN is hexagonal boron nitride), valley relaxation is
found to be monoexponential. The valley relaxation time $\tau_v$ is quite long
($\sim$10~$\mu$s) at low carrier densities, but decreases rapidly to less than
100~ns at high electron or hole densities $\gtrsim$2 $\times
10^{12}$~cm$^{-2}$. In contrast, in a partially-encapsulated WSe$_2$ monolayer
placed directly on silicon dioxide (hBN/WSe$_2$/SiO$_2$), carrier valley
relaxation is multi-exponential at low carrier densities. The difference is
attributed to environmental disorder from the SiO$_2$ substrate. Unexpectedly,
very small out-of-plane magnetic fields can increase $\tau_v$, especially in
the hBN/WSe$_2$/SiO$_2$ structure, suggesting that localized states induced by
disorder can play an important role in depolarizing spins and mediating the
valley relaxation of resident carriers in monolayer transition
metal-dichalcogenide semiconductors.
