Electrodynamics of Abrikosov vortices: the Field Theoretical Formulation

TL;DR

This paper presents a unified field theoretical approach to the electrodynamics of Abrikosov vortices in superconductors, deriving concise equations and exploring novel gauge field characteristics.

Contribution

It introduces a relativistic worldsheet formulation for vortices, unifying various electrodynamic effects and extending the framework to two-form sources without electric monopoles.

Findings

Derived simple equations for vortex electrodynamics.

Connected vortex dynamics to gauge field properties.

Revealed potential for unexpected phenomena in the new framework.

Abstract

Electrodynamic phenomena related to vortices in superconductors have been studied since their prediction by Abrikosov, and seem to hold no fundamental mysteries. However, most of the effects are treated separately, with no guiding principle. We demonstrate that the relativistic vortex worldsheet in spacetime is the object that naturally conveys all electric and magnetic information, for which we obtain simple and concise equations. Breaking Lorentz invariance leads to down-to-earth Abrikosov vortices, and special limits of these equations include for instance dynamic Meissner screening and the AC Josephson relation. On a deeper level, we explore the electrodynamics of two-form sources in the absence of electric monopoles, in which the electromagnetic field strength itself acquires the characteristics of a gauge field. This novel framework leaves room for unexpected surprises.