Topological aspects of dual superconductors

TL;DR

This paper explores the topological properties of two-gap superconductors, examining their connection to phenomena like flux quantization and the Meissner effect, and discusses knotted string geometries using topological invariants.

Contribution

It introduces a topological framework for understanding dual superconductors, linking their properties to knot theory and gauge invariants, with and without Josephson coupling.

Findings

Topological aspects influence flux quantization and Meissner effect.

Knotted string geometries are characterized by Hopf invariants.

Topological features depend on the gauge group structure.

Abstract

We discuss topological aspects of two-gap superconductors with and without Josephson coupling between gaps. We address nontrivial topological aspects of the dual superconductors and its connections to Meissner effect and flux quantization. The topological knotted string geometry is also discussed in terms of the Hopf invariant, curvature and torsion of the strings associated with U(1)$\times$U(1) gauge group.