  We develop a general theoretical framework of integrated paired
photon-plasmon generation through spontaneous wave mixing in nonlinear
plasmonic and metamaterial nanostructures, rigorously accounting for material
dispersion and losses in quantum regime through the electromagnetic Green
function. We identify photon-plasmon correlations in layered metal-dielectric
structures with 70% internal heralding quantum efficiency, and reveal novel
mechanism of broadband generation enhancement due to topological transition in
hyperbolic metamaterials.
