Strong-light matter coupling and exciton-polaritons via the retarded Bethe-Salpeter Equation*

Strong light-matter coupling in the form of exciton-polaritons, a hybrid state with mixed excitonic and photonic character, has recently generated significant interest as a potentially powerful way to tune the optoelectronic and chemical properties of materials. Previous efforts to study exciton-polaritons from first-principles have relied on a perturbative treatment of excitons as an effective screening of the photon. Introducing light-matter coupling in such a manner assumes the presence of an exchange interaction between excitons, and subsequently fails to capture both bright excitons capable of forming exciton-polaritons and their dark counterparts, as well as their associated quasiparticle wavfunctions. Here we develop an explicitly retarded and gauge invariant formulation of the Bethe-Salpeter equation to treat exciton-polaritons and dark excitons on equal footing in a non-perturbative many-body approach. We apply our formalism to MgO and pentacene, where we observe a dramatic renormalization of the exciton dispersion and a previously unpredicted attractive exchange interaction. By solving the retarded Bethe-Salpeter equation in the regime of attractive exchange, we present the first ab-initio calculation of exciton-polariton wavefunctions and reveal an order of magnitude increase in real-space localization due to light-matter coupling. This work also has important implications for the description of excitons in cavities from first principles.