Topologically Protected Vortex Knots in an Experimentally Realizable System

TL;DR

This paper demonstrates the existence of topologically protected vortex knots in experimentally realizable systems like spin-2 Bose-Einstein condensates and bent-core nematic liquid crystals, showcasing novel topological structures.

Contribution

It introduces the first known examples of vortex knots with topological protection in systems that can be realized experimentally.

Findings

Topologically protected vortex knots are constructed in spin-2 Bose-Einstein condensates.

Similar vortex knots are found in bent-core nematic liquid crystals.

These knots cannot decay into simple loops without destroying the phase.

Abstract

Ordered media often support vortex structures with intriguing topological properties. Here, we investigate non-Abelian vortices in tetrahedral order, which appear in the cyclic phase of spin-2 Bose--Einstein condensates and in the tetrahedratic phase of bent-core nematic liquid crystals. Using these vortices, we construct topologically protected knots in the sense that they cannot decay into unlinked simple loop defects through vortex crossings and reconnections without destroying the phase. The discovered structures are the first examples of knots bearing such topological protection in a known experimentally realizable system.