Fluctuation-induced electromagnetic response of type-II superconductors from coupled London condensate and Abrikosov vortex dynamics

We develop a theoretical framework for fluctuation-induced Casimir-Lifshitz interactions between two type-II superconducting plates in the mixed state, based on a unified electrodynamic response including two coupled fluctuation channels: the London condensate and Abrikosov vortex dynamics. The effective dielectric function is obtained by combining London theory with a generalized vortex response model including inertia, pinning, and dissipation. Both contributions enter on equal footing and determine the electromagnetic response of the system.From this response, we calculate the fluctuation-induced pressure in the non-retarded and retarded regimes. It is shown that vortex mobility modifies the spectral response and reduces the interaction strength, while pinning and damping enhance it by suppressing vortex dynamics. Static magnetic contributions (Meissner screening and inter-plate vortex-vortex interaction) are considered separately and dominate at typical fields.