Optical N-invariant of graphene’s topological viscous Hall fluid

Over the past three decades, graphene has become the prototypical platform for discovering topological phases of matter. Both the Chern $$C\in {\mathbb{Z}}$$ C ∈ Z and quantum spin Hall $$\upsilon \in {{\mathbb{Z}}}_{2}$$ υ ∈ 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 $$N\in {\mathbb{Z}}$$ N ∈ 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.

Hall viscosity and conductivity of two-dimensional chiral superconductors

We compute the Hall viscosity and conductivity of non-relativistic two-dimensional chiral superconductors, where fermions pair due to a short-range attractive potential, e.g. \boldsymbol{p+\mathrm{i}p}𝐩+i𝐩 pairing, and interact via a long-range repulsive Coulomb force. For a logarithmic Coulomb potential, the Hall viscosity tensor contains a contribution that is singular at low momentum, which encodes corrections to pressure induced by an external shear strain. Due to this contribution, the Hall viscosity cannot be extracted from the Hall conductivity in spite of Galilean symmetry. For mixed-dimensional chiral superconductors, where the Coulomb potential decays as inverse distance, we find an intermediate behavior between intrinsic two-dimensional superconductors and superfluids. These results are obtained by means of both effective and microscopic field theory.