Reduction of the electrodynamics of superconductors to those for conductors with the incorporation of spatial dispersion

TL;DR

This paper derives the frequency-dependent surface impedance of superconductors by incorporating spatial dispersion, revealing that perfect conductors exhibit the Meissner effect similarly to superconductors.

Contribution

It introduces a framework that reduces the electrodynamics of superconductors to that of conductors with spatial dispersion, highlighting the emergence of the Meissner effect.

Findings

Spatial dispersion affects surface impedance frequency dependence.

Perfect conductors can exhibit the Meissner effect when spatial dispersion is considered.

The approach unifies the electrodynamics of superconductors and perfect conductors.

Abstract

We derive general frequency dependencies of the surface impedance modulus for conductors without the dc dissipation, i. e. for superconductors or perfect conductors. The frequency-dependent surface impedance was applied for the solutions corresponding to the spatially dispersive eigenvalues of the permittivity operator for conductors. We demonstrate that appropriately taken into account effects of the spatial dispersion can give the general frequency dependence of the surface impedance for the obtained solutions including that for superconductor. It is shown that an incorporation of the spatial dispersion leads to an appearance of the Meissner effect in perfect conductors in the same manner as in superconductors.