Dynamical Excitonic Effects in Doped Two-Dimensional Semiconductors

It is well-known that excitonic effects can dominate the optical properties of two-dimensional materials. These effects, however, can be substantially modified by doping free carriers. We investigate these doping effects by solving the first-principles Bethe-Salpeter Equation. Dynamical screening effects, included via the sum-rule preserving generalized plasmon-pole model, are found to be important in the doped system. Using monolayer $\mathrm{MoS_2}$ as an example, we find that upon moderate doping, the exciton binding energy can be tuned by a few hundred meVs, while the exciton peak position stays nearly constant due to a cancellation with the quasiparticle band gap renormalization. At higher doping densities, the exciton peak position increases linearly in energy and gradually merges into a Fermi-edge singularity. Our results are crucial for the quantitative interpretation of optical properties of two-dimensional materials and the further development of ab initio theories of studying charged excitations such as trions.