Tunable surface electromagnetic waves at a graphene–hypercrystal boundary under magnetic bias

Transverse magnetic (TM) and transverse electric (TE) surface electromagnetic waves supported by a graphene-hypercrystal interface are studied in the presence of an external static magnetic field. The system consists of a graphene monolayer placed at the interface between vacuum and a magnetoactive ferrite-semiconductor layered metamaterial described within the effective medium approximation. The magnetic field is applied parallel to the graphene plane (Voigt configuration), so that the Hall conductivity in graphene is absent and the graphene response is governed by a scalar surface conductivity. The optical conductivity of graphene is described using the intraband (Drude) limit of the Kubo formula, which is valid in the considered frequency range. Based on Maxwell's equations, analytical dispersion relations for TM- and TE-polarized surface waves are derived. The obtained expressions explicitly demonstrate the distinct roles of graphene in the two polarizations, leading to different conductivity-dependent contributions to the dispersion laws. It is shown that the combined action of graphene and the anisotropic magnetoactive hypercrystal enables flexible control over the existence domains, dispersion characteristics, and field localization of surface waves. These results highlight the potential of graphene-hypercrystal interfaces as tunable platforms for controlling surface electromagnetic modes in the terahertz and mid-infrared frequency ranges.