Dynamics and Effective Actions of BCS Superconductors

TL;DR

This paper develops effective dynamical theories for metals and BCS superconductors, covering different temperature regimes and impurity conditions, with a focus on gauge invariance and particle-hole asymmetry effects.

Contribution

It introduces a comprehensive effective action formalism for BCS superconductors, incorporating temperature, impurity effects, and band structure asymmetries.

Findings

Effective actions derived for both metallic and superconducting regimes.

Gauge-invariant formulation of electrodynamics in superconductors.

Analysis of particle-hole asymmetry impacts on superconductor dynamics.

Abstract

We derive effective dynamical theories for metals and BCS superconductors, based on the effective action formalism. Both the metallic regime $T\gtrsim T_{C}$ and the superconducting regime $T\ll T_{C}$ are studied in the clean and dirty limit. Furthermore, we consider the effect of particle-hole asymmetry in the band structure. Using gauge invariance, the electrodynamics of the problem is formulated in a transparent way. The effective actions are useful starting points for treating dynamical problems involving BCS superconductors.