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Ordered media often support vortex structures with intriguing topologicalproperties. Here, we investigate non-Abelian vortices in tetrahedral order,which appear in the cyclic phase of spin-2 Bose--Einstein condensates and inthe tetrahedratic phase of bent-core nematic liquid crystals. Using thesevortices, we construct topologically protected knots in the sense that theycannot decay into unlinked simple loop defects through vortex crossings andreconnections without destroying the phase. The discovered structures are thefirst examples of knots bearing such topological protection in a knownexperimentally realizable system.

Topologically Protected Vortex Knots in an Experimentally Realizable System