Optical <i>N-</i>invariant of graphene's viscous Hall fluid

Over the past three decades, graphene has become the prototypical platform for discovering unique phases of topological matter. Both the Chern and Z2 insulator were first predicted in graphene, which led to a veritable explosion of research in topological materials. Here, we introduce a new topological classification of two-dimensional matter - the optical N-phases. The Chern and Z2 phases are related to charge and spin transport respectively, whereas the N-phases are connected to polarization transport. We prove that graphene's viscous Hall fluid is optically nontrivial with the underlying physical mechanism being Hall viscosity. We discover spin-1 Neel-type skyrmions in the bulk magnetoplasma and a deep sub-wavelength phenomenon reminiscent of the Meissner effect. We also propose a novel probe of topological matter, evanescent magneto-optic Kerr effect (e-MOKE) spectroscopy. Lastly, we rigorously analyze the boundary physics which reveals gapless edge magnetoplasmons that are immune to back-scattering and navigate sharp defects with impunity.