Spin-1 Photonic Skyrmion in Viscous Quantum Hall Fluids

We present the fundamental model of a topological electromagnetic phase of matter: viscous Maxwell-Chern-Simons theory. We demonstrate that this is the minimal (exactly solvable) gauge theory with a nontrivial photonic Chern number. The interplay of symmetry and topology is also captured in the Chern number, which is determined by the spin-1 representations of a photonic skyrmion at high-symmetry points in the Brillouin zone. Physically, our predicted electromagnetic phases are connected to a dynamical photonic mass in a viscous quantum Hall fluid. The electromagnetic phase is topologically nontrivial 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.