Non-Meissner electrodynamics and knotted solitons in two-component superconductors

TL;DR

This paper investigates the properties and stability of knotted solitons in two-component superconductors, introducing a new perturbative approach and identifying conditions under which these solitons can be stable at certain length scales.

Contribution

It presents a novel perturbative method to analyze knotted solitons in multicomponent superconductors and demonstrates their potential stability at intermediate length scales.

Findings

Existence of a length scale where electrodynamics is dominated by a self-induced Faddeev term.

Knotted solitons are unstable at short scales but can be stable at intermediate scales.

High topological charge configurations may be more stable than low-charge ones.

Abstract

I consider electrodynamics and the problem of knotted solitons in two-component superconductors. Possible existence of knotted solitons in multicomponent superconductors was predicted several years ago. However their basic properties and stability in these systems remains an outstandingly difficult question both for analytical and numerical treatment. Here I propose a new perturbative approach to treat self-consistently all the degrees of freedom in the problem. I show that there exists a length scale for a Hopfion texture where the electrodynamics of a two-component superconductor is dominated by a self-induced Faddeev term, which is a stark contrast to the Meissner electrodynamics of single-component systems. I also show that at certain short length scales knotted solitons in two-component Ginzburg-Landau model are not described by a Faddeev-Skyrme-type model and are unstable. However these solitons can be stable at some intermediate length scales. I argue that configurations with a high topological charge may be more stable in this system than low-topological-charge configurations. In the second part of the paper I discuss qualitatively different physics of the stability of knotted solitons in a more general Ginzburg-Landau model and point out the physically relevant terms which enhance or suppress stability of the knotted solitons. With this argument it is demonstrated that the generalized Ginburg-Landau model possesses stable knotted solitons.