▎ 摘　　要

Over the past three decades, graphene has become the prototypical platform for discovering topological phases of matter. Both the Chern C is an element of Z and quantum spin Hall upsilon is an element of Z2 insulators were first predicted in graphene, which led to a veritable explosion of research in topological materials. We introduce a new topological classification of two-dimensional matter - the optical N-phases N is an element of Z. This topological quantum number is connected to polarization transport and captured solely by the spatiotemporal dispersion of the susceptibility tensor chi. We verify N not equal 0 in graphene with the underlying physical mechanism being repulsive Hall viscosity. An experimental probe, evanescent magneto-optic Kerr effect (e-MOKE) spectroscopy, is proposed to explore the N-invariant. We also develop topological circulators by exploiting gapless edge plasmons that are immune to back-scattering and navigate sharp defects with impunity. Our work indicates that graphene with repulsive Hall viscosity is the first candidate material for a topological electromagnetic phase of matter. Graphene is the archetype for realizing two-dimensional topological phases of matter. Here, the authors introduce a new topological classification connected to polarization transport, where the topological number is revealed in the spatiotemporal dispersion of the susceptibility tensor.