Ab initio formalism for exciton-polaritons in two-dimensional materials*

The presence of tightly-bound and long-lived excitons in two dimensional materials have motivated recent interest in tuning material optoelectronic properties. Critical to these properties is the dispersion of excitons with respect to the center-of-mass momentum, which can be dramatically affected by hybridization with light to form exciton-polaritons. The two dimensional nature of the material relaxes the constraint of momentum conservation in the out-of-plane direction and warrants a detailed treatment of this light-matter coupling. In this work, we carefully consider polaritonic effects by treating the retarded exchange interaction in the electron-hole interaction kernel using a mixed space photon propagator. Our first principles calculations using the Bethe-Salpeter equation formalism captures frequency- and momentum-dependent features near the light cone of monolayer MoS₂. We find that the exciton-polariton dispersion is significantly altered when the retarded exchange interaction is considered. In particular, we find that inside the light cone the exciton-polariton is predicted to have a finite lifetime and little renormalization of its dispersion, a unique feature resulting from the dimensionality of the system. We expect our results to have important implications for the understanding of excitons in 2D materials, their thermalization, and dynamics.