Doping-induced non-Markovian interference causes excitonic linewidth broadening in monolayer WSe$_2$

Strong Coulomb interactions in atomically thin semiconductors like monolayer WSe$_2$ induce not only tightly bound excitons, but also make their optical properties very sensible to doping. By utilizing a microscopic theory based on the excitonic Heisenberg equations of motion, we systematically determine the influence of doping on the excitonic linewidth, lineshift, and oscillator strength. We calculate trion resonances and demonstrate that the Coulomb coupling of excitons to the trionic continuum generates a non-Markovian interference, which, due to a time retardation, builds up a phase responsible for asymmetric exciton line shapes and increased excitonic linewidths. Our calculated doping dependence of exciton and trion linewidths, lineshifts, and oscillator strengths explains recent experiments. The gained insights provide the microscopic origin of the optical fingerprint of doped atomically thin semiconductors.