Topologically Protected Vortex Knots in an Experimentally Realizable System

Ordered media often support vortex structures with intriguing topological properties. Here, we investigate non-Abelian vortices in tetrahedral order using the mathematical formalism of colored links. Due to the generality of our methods, the results apply to all physical systems governed by tetrahedral order, such as the cyclic phase of spin-2 Bose-Einstein condensates and 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.