Different length-scales for order parameters in two-gap superconductors: the extended Ginzburg-Landau theory

TL;DR

This paper extends the Ginzburg-Landau theory to next-to-leading order to numerically analyze the healing lengths of two order parameters in two-gap superconductors, revealing significant differences that justify the theory's use.

Contribution

The paper introduces an extended Ginzburg-Landau model that accurately captures distinct healing lengths of two-gap superconductors with minimal additional computational complexity.

Findings

Healing lengths can differ significantly between the two order parameters.

The extended model remains computationally efficient compared to microscopic approaches.

The theory justifies its applicability to real two-gap superconductor physics.

Abstract

Using the Ginzburg-Landau theory extended to the next-to-leading order we determine numerically the healing lengths of the two order parameters at the two-gap superconductor/normal metal interface. We demonstrate on several examples that those can be significantly different even in the strict domain of applicability of the Ginzburg-Landau theory. This justifies the use of this theory to describe relevant physics of two-gap superconductors, distinguishing them from their single-gap counterparts. The calculational degree of complexity increases only slightly with respect to the conventional Ginzburg-Landau expansion, thus the extended Ginzburg-Landau model remains numerically far less demanding compared to the full microscopic approaches.