Optical $N$-invariant of graphene's viscous Hall fluid

Abstract

Over the past three decades, graphene has become the prototypical platform for discovering unique phases of topological matter. Both the Chern insulator $C\in \mathbb{Z}$ and the quantum spin Hall insulator $\nu \in {\mathbb{Z}}_2$ were first predicted in graphene, which led to a veritable explosion of research in topological materials. Here, we introduce a new topological classification of two-dimensional matter -- the optical $N$-phases $N\in \mathbb{Z}$. The $C$ and $\nu$ phases are related to charge and spin transport respectively, whereas the $N$-phases are connected to polarization transport. In all three cases, transportation of charge/spin/polarization quanta is forbidden in the bulk but permitted on the edge. One fundamental difference is that the $N$-invariant is defined for dynamical electromagnetic waves over all Matsubara frequencies and wavevectors. We show this topological quantum number is captured solely by the spatiotemporal dispersion of the susceptibility tensor $\chi (\omega ,\mathbf{q})$. We also prove $N\ne 0$ is nontrivial in graphene's viscous Hall fluid with the underlying physical mechanism being Hall viscosity ${\eta }_H$. In the nontrivial phase, we discover a deep sub-wavelength phenomenon reminiscent of the Meissner effect: at a particularly large photon momentum $q=D_H^{-1}$ defined by the Hall diffusion length $D_H$, the magnetic field is completely expelled from the viscous Hall fluid. We propose a new probe of topological matter, evanescent magneto-optic Kerr effect (e-MOKE) spectroscopy, to unravel this novel optical $N$-invariant and verify the magnetic field expulsion. Our work indicates that graphene with Hall viscosity is the first candidate material for a topological electromagnetic phase of matter.

arXiv comment8 pages, 5 figures, 1 table

References in corpus (46)

• Quantum Spin Hall Effect in Graphene
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Negative local resistance caused by viscous electron backflow in graphene
• Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene
• Synthetic Dimension in Photonics
• Viscosity of Quantum Hall Fluids
• Single particle Green's functions and interacting topological insulators
• Electron Viscosity, Current Vortices and Negative Nonlocal Resistance in Graphene
• Quantized Faraday and Kerr rotation and axion electrodynamics of a 3D topological insulator
• Experimental realization of a Weyl exceptional ring
• Odd viscosity in chiral active fluids
• Hall Viscosity and Electromagnetic Response
• Measuring Hall Viscosity of Graphene's Electron Fluid
• Hall viscosity, orbital spin, and geometry: paired superfluids and quantum Hall systems
• Kubo formulas for viscosity: Hall viscosity, Ward identities, and the relation with conductivity
• Antiskyrmions stabilized at interfaces by anisotropic Dzyaloshinskii-Moriya interaction
• Sum Rules for the Optical and Hall Conductivity in Graphene
• Slip flow over structured surfaces with entrapped microbubbles
• Negative magnetoresistance in viscous flow of two-dimensional electrons
• Topological waves in fluids with odd viscosity
• Topological Order Parameters for Interacting Topological Insulators
• Hydrodynamic Electron Flow and Hall Viscosity
• Fluidity Onset in Graphene
• Torsional Anomalies, Hall Viscosity, and Bulk-boundary Correspondence in Topological States
• Non-local transport and the Hall viscosity of 2D hydrodynamic electron liquids
• The boundary conditions of viscous electron flow
• Transport signatures of Hall viscosity
• Anomalous bulk-edge correspondence in continuous media
• Photonic Dirac monopoles and skyrmions: spin-1 quantization
• Magnetohydrodynamics in graphene: shear and Hall viscosities
• Hydrodynamic Model for Conductivity in Graphene
• Topology and Observables of the Non-Hermitian Chern Insulator
• Continuous bulk and interface description of topological insulators
• Quantum gyro-electric effect: Photon spin-1 quantization in continuum topological bosonic phases
• Hall viscosity and electromagnetic response of electrons in graphene
• Disorder-immune photonics based on Mie-resonant dielectric metamaterials
• Hall and dissipative viscosity effects on edge magnetoplasmons
• Topological Interface between Pfaffian and anti-Pfaffian Order in $\nu =5/2$ Quantum Hall Effect
• Magnetoelasticity theory of incompressible quantum Hall liquids
• Indifferent electromagnetic modes: bound states and topology
• Berry phase and anomalous velocity of Weyl fermions and Maxwell photons
• Viscous Maxwell-Chern-Simons theory for topological electromagnetic phases of matter
• Hall viscosity and conductivity of two-dimensional chiral superconductors
• Hall viscosity in the A-phase of superfluid ${}^3$He
• Note on Green Function Formalism and Topological Invariants
• Screening and plasma oscillations in an electron gas in the hydrodynamic approximation

Cited by in corpus (8)

• Photonic spin lattices: symmetry constraints for skyrmion and meron topologies
• Hydrodynamic approach to two-dimensional electron systems
• Roadmap for Photonics with 2D Materials
• Optical $N$-insulators: topological obstructions in the atomistic susceptibility tensor
• Pico-photonics: Anomalous Atomistic Waves in Silicon
• Generalized topological bulk-edge correspondence in bulk-Hermitian continuous systems with non-Hermitian boundary conditions
• Optical N-plasmon: Topological hydrodynamic excitations in Graphene from repulsive Hall viscosity
• Giant resonant skew scattering of plasma waves in a two-dimensional electron gas