Todd Van Mechelen, Wenbo Sun, and Zubin Jacob. 8/5/2021. Optical N-invariant of graphene’s topological viscous Hall fluid. Nature Communications, 12, 4729.

Over the past three decades, graphene has become the prototypical platform for discovering topological phases of matter. Both the Chern C 2 Z and quantum spin Hall υ 2 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 2 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.