Only-phase Popov action: thermodynamic derivation and superconducting electrodynamics

TL;DR

This paper derives the thermodynamic basis of the only-phase Popov action for superfluids, applies it to superconductors, and predicts electrostatic field decay with implications for superconducting electrodynamics.

Contribution

It provides a thermodynamic derivation of the Popov action and extends its application to superconductors coupled with electromagnetic fields.

Findings

Electrostatic field decays inside superconductors with a length scale smaller than the London penetration depth.

The theory predicts specific electromagnetic behavior in charged superfluids.

The derivation confirms results using a relativistic version from the Klein-Gordon Lagrangian.

Abstract

We provide a thermodynamic derivation of the only-phase Popov action functional, which is often adopted to study the low-energy effective hydrodynamics of a generic nonrelativistic superfluid. It is shown that the crucial assumption is the use of the saddle point approximation after neglecting the quantum-pressure term. As an application, we analyze charged superfluid (superconductors) coupled to the electromagnetic field at zero temperature. Our only-phase and minimally-coupled theory predicts the decay of the electrostatic field inside a superconductor with a characteristic length much smaller than the London penetration depth of the static magnetic field. This result is confirmed also by a relativistic only-phase Popov action we obtain from the Klein-Gordon Lagrangian.