The Gradient Expansion for the Free-Energy of a Clean Superconductor

TL;DR

This paper introduces a new method to derive the gradient expansion of the free energy in clean BCS superconductors, providing explicit results up to fourth order in the order parameter gradients.

Contribution

A novel method for calculating the gradient expansion of the free energy in superconductors, with explicit higher-order results.

Findings

Explicit fourth-order gradient expansion results

A new computational approach for superconductor free energy

Enhanced understanding of spatial variations in superconductors

Abstract

We describe a novel method for obtaining the gradient expansion for the free energy of a clean BCS superconductor. We present explicit results up to fourth order in the gradients of the order parameter.