A flux-based 3D electrodynamic modeling approach to superconducting circuits and materials

The flux-based description of superconducting lumped-element circuits has enjoyed tremendous success in studying the fundamental physics of superconducting devices and circuits as well as their computational modeling. We extend flux-based electrodynamic field theory of superconductors to two- and three-dimensional materials and fields. Starting with Maxwell's equations and superconducting order parameter equations, we derive equations of motion for gauge-invariant flux fields describing the dynamics of hybridized light-matter fields. The formulation utilizes a dual-mesh construction with flux fields and currents living on edges and charges living on nodes, enabling accurate charge-conserving dynamics. We demonstrate its application to the Meissner effect and flux quantization in 3D superconducting structures.