Quantum theory of two-dimensional materials coupled to electromagnetic resonators

We present a microscopic quantum theory of light-matter interaction in pristine sheets of two-dimensional semiconductors coupled to localized electromagnetic resonators such as optical nanocavities or plasmonic particles. The light-matter interaction breaks the translation symmetry of excitons in the two-dimensional lattice, and we find that this symmetry-breaking interaction leads to the formation of a localized exciton state, which mimics the spatial distribution of the electromagnetic field of the resonator. The localized exciton state is in turn coupled to an environment of residual exciton states. We quantify the influence of the environment and find that it is most pronounced for small lateral confinement length scales of the electromagnetic field in the resonator, and that environmental effects can be neglected if this length scale is sufficiently large. The microscopic theory provides a physically appealing derivation of the coupled oscillator models widely used to model experiments on these types of systems, in which all observable quantities are directly derived from the material parameters and the properties of the resonant electromagnetic field. As a consistency check, we show that the theory recovers the results of semiclassical electromagnetic calculations and experimental measurements of the excitonic dielectric response in the linear excitation limit. The theory, however, is not limited to linear response, and in general describes nonlinear exciton-exciton interactions in the localized exciton state, thereby providing a powerful means of investigating the nonlinear optical response of such systems.