Hybridization of edge modes with substrate phonons

Surface plasmons or phonons propagating on a two-dimensional (2D) material can exhibit coupling with resonant excitations in its substrate, and the resulting coupled modes were extensively studied. Similar coupling of edge modes propagating along a boundary of 2D material with the substrate excitations remains unexplored. This paper aims to bridge this gap by investigating the edge-substrate hybrid modes using the exact Wiener-Hopf analytical approach. We analyze dispersions, decay rate, and confinement of such hybrid modes both without magnetic field (plasmon-phonon and phonon-phonon hybrid modes) and in quantizing magnetic field where edge magnetoplasmons hybridize with substrate phonons. The hybrid modes are predicted to occur in THz and far-IR ranges for several combinations of quasi-2D materials (single- and bilayer graphene, quantum wells, thin-film semiconductors) and substrates with polar-phonon resonances.