Electrodynamics of s-wave superconductors

TL;DR

This paper derives a comprehensive set of equations describing the electrodynamics of s-wave superconductors, integrating relativistic and non-relativistic formalisms to analyze electromagnetic effects on superconductivity.

Contribution

It introduces a novel gauge-invariant four-vector field into the electrodynamics equations, providing a unified framework for superconducting electromagnetic phenomena.

Findings

Magnetic fields suppress superconductivity.

Electric fields support superconductivity.

The dual four-vector field is central to the theory.

Abstract

In this paper we give a derivation of a system of equations to describe the electrodynamics of s-wave superconductors. First, we consider a relativistically covariant theory in terms of gauge four-vector electromagnetic potential and scalar complex field. We use the first-order formalism to obtain the supplemented Maxwell equations for gauge invariant electric, magnetic, four-vector fields and the modulus of the superconducting order parameter. The new four-vector field appears in some of the equations as a gauge invariant super-current and in other ones, while gauge invariant, as a four-vector electromagnetic potential. This dual contribution of the new four-vector field is the basis of the electrodynamics of superconductors. We focus on the system of equations with time-independent fields. The qualitative analysis shows that the applied magnetic field suppresses the superconductivity, while the applied electric field impacts appositely, supporting it. Second we consider time-dependent non-relativistic Ginzburg-Landau theory.