Vortex Dynamics within the BCS Theory

TL;DR

This paper derives vortex dynamics within BCS theory, confirming the transverse force and friction results, and discusses errors in previous microscopic derivations, applicable across different limits and temperatures.

Contribution

It provides a path integral derivation of vortex forces within BCS theory, validating previous results and addressing errors in earlier microscopic approaches.

Findings

Transverse force matches Ao and Thouless's Berry phase result

Friction aligns with Bardeen and Stephen's findings

Derivation valid in both clean and dirty limits at all temperatures

Abstract

We outline a conventional path integral derivation of the transverse force and the friction for a vortex in a superconductor based on the BCS theory. The derivation is valid in both clean and dirty limits at both zero and finite temperatures. The transverse force is found to be precisely as what has been obtained by Ao and Thouless using the Berry's phase method. The friction is essentially the same as the Bardeen and Stephen's result. Errors in some previous representive microscopic derivations are discussed.