  The ultrathin transition metal dichalcogenides (TMDs) have emerged as
promising materials for various applications using two dimensional (2D)
semiconductors. They have attracted increasing attention due to their unique
optical properties originate from neutral and charged excitons. Here, we report
negatively charged exciton formation in monolayer TMDs, notably tungsten
disulfide WS2. Our theory is based on an effective mass model of neutral and
charged excitons, parameterized by ab-initio calculations. Taking into the
account the strong correlation between the monolayer WS2 and the surrounding
dielectric environment, our theoretical results are in good agreement with
one-photon photoluminescence (PL) and reflectivity measurements. We also show
that the exciton state with p-symmetry, experimentally observed by two-photon
PL emission, is energetically below the 2s-state. We use the equilibrium mass
action law, to quantify the relative weight of exciton and trion PL. We show
that exciton and trion emission can be tuned and controlled by external
parameters like temperature, pumping and injection electrons. Finally, in
comparison with experimental measurements, we show that exciton emission in
monolayer tungsten dichalcogenides is substantially reduced. This feature
suggests that free exciton can be trapped in disordered potential wells to form
a localized exciton and therefore offers a route toward novel optical
properties.
