Graphene is a unique material to study fundamental limits of plasmonics. Apart from the ultimate single-layer thickness, its carrier concentration can be tuned by chemical doping or applying an electric field. In this manner the electrodynamic proper
ties of graphene can be varied from highly conductive to dielectric. Graphene supports strongly confined, propagating surface plasmon-polaritons (SPPs) in a broad spectral range from terahertz to mid-infrared frequencies. It also possesses a strong magneto-optical response and thus provides complimentary architectures to conventional magneto-plasmonics based on magneto-optically active metals or dielectrics. Despite of a large number of review articles devoted to plasmonic properties and applications of graphene, little is known about graphene magneto-plasmonics and topological effects in graphene-based nanostructures, which represent the main subject of this review. We discuss several strategies to enhance plasmonic effects in topologically distinct closed surface landscapes, i.e. graphene nanotubes, cylindric nanocavities and toroidal nanostructures. A novel phenomenon of the strongly asymmetric SPP propagation on chiral meta-structures and fundamental relations between structural and plasmonic topological indices are reviewed.
Non-reciprocity and asymmetric transmission in optical and plasmonic systems is a key element for engineering the one-way propagation structures for light manipulation. Here we investigate topological nanostructures covered with graphene-based meta-s
urfaces, which consist of a periodic pattern of sub-wavelength stripes of graphene winding around the (meta-) tube or (meta-)torus. We establish the relation between the topological and plasmonic properties in these structures, as justified by simple theoretical expressions. Our results demonstrate how to use strong asymmetric and chiral plasmonic responses to tailor the electrodynamic properties in topological meta-structures. Cavity resonances formed by elliptical and hyperbolic plasmons in meta-structures are sensitive to the one-way propagation regime in a finite length (Fabry-Perot-like) meta-tube and display the giant mode splitting in a (Mach-Zehnder-like) meta-torus.
