Viscous Topological Electromagnetic Phases of Matter

We present the fundamental model of a topological electromagnetic phase of matter: viscous Maxwell-Chern-Simons theory. 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 for electromagnetic waves coupled to matter $C\neq 0$. 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 $C\neq 0$ leading to unidirectional transverse electromagnetic edge waves 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.