Excitons in a hyperbolic medium

We study the interaction between excitons in a two-dimensional semiconductor and phonons in an anisotropic polar insulator that behaves as a hyperbolic medium. We show that the energy levels of the excitons are renormalized due to polaron-like effects. The excited states of excitons can either form quasi-bound complexes with phonons or exhibit an enhanced decay rate in the hyperbolic frequency region. Coupling to phonons also modifies van der Waals interaction, Förster resonant energy transfer, and collective mode dispersion of excitons. We discuss how these effects may be observed in optical experiments and their possible nanophotonic applications.