Theory of phonon sidebands in the absorption spectra of moiré exciton-polaritons

Abstract: Excitons in twisted bilayers of transition metal dichalcogenides have strongly modified dispersion relations due to the formation of periodic moir\'e potentials. The strong coupling to a light field in an optical cavity leads to the appearance of moir\'e polaritons. In this paper, we derive a theoretical model for the linear absorption spectrum of the coupled moir\'e polariton-phonon system based on the time-convolutionless (TCL) approach. Results obtained by numerically solving the TCL equation are compared to those obtained in the Markovian limit and from a perturbative treatment of non-Markovian corrections. A key quantity for the interpretation of the findings is the generalized phonon spectral density. We discuss the phonon impact on the spectrum for realistic moir\'e exciton dispersions by varying twist angle and temperature. Key features introduced by the coupling to phonons are broadenings and energy shifts of the upper and lower polariton peak and the appearance of phonon sidebands between them. We analyze these features with respect to the role of Markovian and non-Markovian effects and find that they strongly depend on the twist angle. We can distinguish between the regimes of large, small, and intermediate twist angles. In the latter phonon effects are particularly pronounced due to dominating phonon transitions into regions which are characterized by van Hove singularities in the density of states.