  Embedding a monolayer of a transition metal dichalcogenide in a high-Q
optical cavity results in the formation of distinct exciton polariton modes.
The polaritons are affected by the strong exciton-phonon interaction in the
monolayer. We use a time convolutionless master equation to calculate the
phonon influence on the spectra of the polaritons. We discuss the non-trivial
dependence of the line shapes of both branches on temperature and detuning. The
peculiar polariton dispersion relation results in a linewidth of the lower
polariton being largely independent of the coupling to acoustic phonons. For
the upper polariton, acoustic phonons lead to a low-energy shoulder of the
resonance in the linear response. Furthermore, we analyze the influence of
inhomogeneous broadening being the dominant contribution to the lower polariton
linewidth at low temperatures. Our results point towards interesting phonon
features in polariton spectra in transition metal dichalcogenides.

Mesoscale and Nanoscale Physics