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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 the 2D material with 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 a 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.