Over the past three decades, graphene has become the prototypical platform for discovering topological phases of matter. Both the Chern C ε Z and quantum spin Hall ν ε 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 ε Z. This topological quantum number is connected to polarization transport and captured solely by the spatiotemporal dispersion of the susceptibility tensor χ. We verify N ≠ 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.
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