Cavity-induced exciton localization and polariton blockade in two-dimensional semiconductors coupled to an electromagnetic resonator

Recent experiments have demonstrated strong light-matter coupling between electromagnetic nanoresonators and pristine sheets of two-dimensional semiconductors, and it has been speculated whether these systems can enter the quantum regime operating at the few-polariton level. To address this question, we present a microscopic quantum theory for the interaction between excitons in a sheet of two-dimensional material and a localized electromagnetic resonator. We find that the light-matter interaction breaks the symmetry of the otherwise translation-invariant system and thereby effectively generates a localized exciton mode, which is coupled to an environment of residual exciton modes. This dissipative coupling increases with tighter lateral confinement, and our analysis reveals this to be a potential challenge in realizing nonlinear exciton-exciton interaction. Nonetheless, we predict that polariton blockade due to nonlinear exciton-exciton interactions is well within reach for nanoresonators coupled to transition-metal dichalcogenides, provided that the lateral confinement can be sufficiently tight to make the nonlinearity overcome the polariton dephasing caused by phonon interactions.