The Ginzburg-Landau theory in application

TL;DR

This paper demonstrates a numerical approach to Ginzburg-Landau theory, reviewing its applications in superconductivity, including thin superconductors and two-gap superconductors, highlighting the influence of coherence lengths on magnetic behavior.

Contribution

It introduces a numerical method for Ginzburg-Landau theory and explores its application to various superconducting systems, emphasizing the role of coherence lengths.

Findings

Numerical approach effectively models superconductivity phenomena.

Two-dimensional GL theory applicable to thin superconductors.

Magnetic behavior depends on coherence length ratios in two-gap superconductors.

Abstract

A numerical approach to Ginzburg-Landau (GL) theory is demonstrated and we review its applications to several examples of current interest in the research on superconductivity. This analysis also shows the applicability of the two-dimensional approach to thin superconductors and the re-defined effective GL parameter kappa. For two-gap superconductors, the conveniently written GL equations directly show that the magnetic behavior of the sample depends not just on the GL parameter of two bands, but also on the ratio of respective coherence lengths.