Knot solitons in modified Ginzburg-Landau model

TL;DR

This paper demonstrates the existence of stable Hopfion solitons in a modified Ginzburg-Landau model, showing their properties resemble those in the Faddeev-Skyrme model and exploring stability mechanisms.

Contribution

It provides the first evidence of stable Hopfions in a modified Ginzburg-Landau model and analyzes their properties and stability mechanisms.

Findings

Hopfions exist as stable solutions up to Hopf invariant 7

Properties closely follow those in Faddeev-Skyrme model

Longer core lengths correlate with increased stability

Abstract

We study a modified version of the Ginzburg-Landau model suggested by Ward and show that Hopfions exist in it as stable static solutions, for values of the Hopf invariant up to at least 7. We also find that their properties closely follow those of their counterparts in the Faddeev-Skyrme model. Finally, we lend support to Babaev's conjecture that longer core lengths yield more stable solitons and propose a possible mechanism for constructing Hopfions in pure Ginzburg-Landau model.