Viscous Maxwell-Chern-Simons theory for topological electromagnetic phases of matter

TL;DR

This paper introduces a viscous Maxwell-Chern-Simons model for topological electromagnetic phases in quantum Hall fluids, revealing topologically protected edge states and connecting Hall viscosity with photonic topology.

Contribution

It presents the first exactly solvable gauge theory with a nontrivial photonic Chern number, linking electromagnetic topological phases to Hall viscosity and spin-1 quantization.

Findings

Discovery of topologically protected chiral edge states

Connection between Hall viscosity and photonic Chern number

Demonstration of a minimal, exactly solvable gauge theory for topological photonics

Abstract

We present the fundamental model of a topological electromagnetic phase of matter: viscous Maxwell-Chern-Simons theory. Our model applies to a quantum Hall fluids with viscosity. We solve both continuum and lattice regularized systems to demonstrate that this is the minimal (exactly solvable) gauge theory with a nontrivial photonic Chern number ($C\neq 0$) for electromagnetic waves coupled to a quantum Hall fluid. The interplay of symmetry and topology is also captured by the spin-1 representations of a photonic skyrmion at high-symmetry points in the Brillouin zone. To rigorously analyze the topological physics, we introduce the viscous Maxwell-Chern-Simons Lagrangian and derive the equations of motion, as well as the boundary conditions, from the principle of least action. We discover topologically-protected chiral (unidirectional) edge states which minimize the surface variation and correspond to massless photonic excitations costing an infinitesimal amount of energy. Physically, our predicted electromagnetic phases are connected to a dynamical photonic mass in the integer quantum Hall fluid. This arises from viscous (nonlocal) Hall conductivity and we identify the nonlocal Chern-Simons coupling with the Hall viscosity. The electromagnetic phase is topologically nontrivial $C\neq 0$ when the Hall viscosity inhibits the total bulk Hall response. Our work bridges the gap between electromagnetic and condensed matter topological physics while also demonstrating the central role of spin-1 quantization in nontrivial photonic phases.