Ginzburg-Landau analysis of the critical temperature and the upper critical field for three-band superconductors

TL;DR

This paper develops a three-band Ginzburg-Landau theory for superconductors, deriving formulas for critical temperature and upper critical field, and analyzing how interband interactions influence these properties.

Contribution

It introduces a novel three-band Ginzburg-Landau framework derived from microscopic Eilenberger equations, highlighting the role of interband interactions.

Findings

Interband interaction sign affects critical temperature and upper critical field.

Derived explicit expressions for Tc and Hc2 in three-band superconductors.

Demonstrated differences from two-band models through analytical and numerical analysis.

Abstract

Using the microscopic formalism of Eilenberger equations, a three-band Ginzburg-Landau theory for the intraband dirty limit and clean interband scattering case is derived. Within the framework of this three-band Ginzburg-Landau theory, expressions for the critical temperature Tc and the temperature dependence of the upper critical field H_c2 are obtained. Based on some special cases of the matrix of interaction constants, we demonstrate the influence of the sign of the interband interaction on the critical temperature and the upper critical field as compared with a two-band superconductor where it plays no role. We study also analytically and numerically the effect of its magnitude.