Hyperbolic Plasmon dispersion and Optical Conductivity of Holey Graphene: signatures of flat-bands

Holey graphene (HG) is a novel two-dimensional (2D) material that has attracted considerable attention due to its remarkable electrical, thermal, and mechanical properties. The recent discovery of flat bands in HG has garnered significant interest. In this work, we systematically investigate the tunable plasmonic modes and optical conductivity of HG at or near the flat band condition by changing the holes radii and periodic configuration. It is found that HG presents nearly flat plasmonic bands in configurations with larger hole radii. Hyperbolic plasmons are found due to the breaking of the graphene's bipartite sublattice symmetry induced by the holes. Such an effect is also confirmed by looking at the optical conductivity, that also presents a marked anisotropy. The material's marked optical anisotropy leads to hyperbolic plasmons, making it a promising platform for nanophotonic applications.