Soliton states in mesoscopic two-band-superconducting cylinders

TL;DR

This paper develops a self-consistent Ginzburg-Landau theory for soliton states in mesoscopic two-band superconducting cylinders, analyzing their stability, energy properties, and potential experimental relevance.

Contribution

It provides the first exact solutions and stability analysis of soliton states in mesoscopic two-band superconductors within the Ginzburg-Landau framework.

Findings

Soliton states are thermodynamically metastable but can have very small energy gaps.

Formation of solitons breaks rotational symmetry and introduces a zero-frequency mode.

The theory applies broadly to mesoscopic doubly-connected two-band superconducting structures.

Abstract

In the framework of the Ginzburg-Landau approach, we present a self-consistent theory of specific soliton states in mesoscopic (thin-walled) two-band-superconducting cylinders in external parallel magnetic fields. Such states arise in the presence of "Josephson-type" interband coupling, when phase winding numbers are different for each component of the superconducting order parameter. We evaluate the Gibbs free energy of the sysyem up to second-order terms in a certain dimensionless parameter $\epsilon\approx\frac{\mathcal{L}_{m}}{\mathcal{L}_{k}}\ll1$, where $\mathcal{L}_{m}$ and $\mathcal{L}_{k} $ are the magnetic and kinetic inductance, respectively. We derive the complete set of exact soliton solutions. These solutions are thoroughly analyzed from the viewpoint of both local and global (thermodynamic) stability. In particular, we show that rotational-symmetry-breaking caused by the formation of solitons gives rise to a zero-frequency rotational mode. Although soliton states prove to be thermodynamically metastable, the minimal energy gap between the lowest-lying single-soliton states and thermodynamically stable zero-soliton states can be much smaller than the magnetic Gibbs free energy of the latter states, provided that intraband "penetration depths" differ substantially and interband coupling is weak. The results of our investigation may apply to a wide class of mesoscopic doubly-connected structures exhibiting two-band superconductivity.