Hyperbolic plasmon dispersion and optical conductivity of holey graphene: Signatures of flat-bands

In this work, we investigate the tunable plasmonic modes and optical conductivity of holey graphene (HG) by varying the radius and periodicity of its perforations. We establish that the breaking of graphene’s bipartite sublattice symmetry is the key physical mechanism, which simultaneously induces electronic flat bands and a strong optical anisotropy. The former gives rise to nearly flat plasmonic bands, while the latter enables the propagation of hyperbolic plasmons. These findings position holey graphene as a promising platform for nanophotonics, offering directional control of light at the nanoscale without the need for complex heterostructures. • Plasmon dispersion in holey graphene is tunable via hole radius and periodicity. • Nearly flat plasmonic bands emerge as a consequence of electronic flat bands. • Sublattice symmetry breaking induces hyperbolic plasmons and strong optical anisotropy. • Holey graphene is presented as a monolithic, 2D platform for hyperbolic plasmonics.