Abstract
Over the past three decades, graphene has become the prototypical platform for discovering topological phases of matter. Both the Chern Cin {mathbb{Z}} and quantum spin Hall upsilon in {{mathbb{Z}}}_{2} 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 Nin {mathbb{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.
Highlights
Over the past three decades, graphene has become the prototypical platform for discovering topological phases of matter
Topological photonics[31,32,33,34] has mainly focused on artificial media like photonic crystals[35,36,37] and metamaterials[38], our findings demonstrate that condensed matter can host topological electromagnetic states
We have introduced the optical phases N 2 Z of twodimensional quantum matter—a topological classification emerging from the invariant optical proprieties of a material
Summary
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. Our work indicates that graphene with repulsive Hall viscosity is the first candidate material for a topological electromagnetic phase of matter. This nontrivial topology is revealed in the magnetohydrodynamics of the 2D Navier–Stokes equations. Quantization of orbital spin[22] and the Wen-Zee shift[23] represent unique topological numbers of these quantum fluids, which are associated with nontrivial electronic states
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