Ginzburg-Landau theory for multiband superconductors: microscopic derivation

TL;DR

This paper develops a microscopic derivation of the Ginzburg-Landau theory for multiband superconductors, providing explicit parameter expressions and exploring symmetry-induced chiral states.

Contribution

It introduces a general procedure to derive GL theory from multiband BCS Hamiltonian with explicit parameters and analyzes chiral states in three-band systems.

Findings

Explicit microscopic expressions for GL parameters.

Symmetry in coupling matrices can lead to chiral ground states.

Demonstrated phase frustration in three-band superconductors.

Abstract

A procedure to derive the Ginzburg-Landau (GL) theory from the multiband BCS Hamiltonian is developed in a general case with an arbitrary number of bands and arbitrary interaction matrix. It combines the standard Gor'kov truncation and a subsequent reconstruction in order to match accuracies of the obtained terms. This reconstruction recovers the phenomenological GL theory as obtained from the Landau model of phase transitions but offers explicit microscopic expressions for the relevant parameters. Detailed calculations are presented for a three-band system treated as a prototype multiband superconductor. It is demonstrated that the symmetry in the coupling matrix may lead to the chiral ground state with the phase frustration, typical for systems with broken time-reversal symmetry.