Reversible Electrically Controlled Fusion of Particle-like Chiral Nematic Vortex Knots

Vortex knots have been seen decaying in many physical systems, despite of the many experimental attemts of obtaining stable vortex knots. Here we describe topologically protected vortex knots in chiral liquid crystals, which remain stable and undergo fusion and fission while conserving a topological invariant. The host medium, a chiral nematic liquid crystal, exhibits intrinsic chirality of the molecular alignment, whereas cores of the vortex lines are structurally achiral regions where molecular twist cannot be defined. We can reversibly switch between fusion and fission of these vortex knots by applying electric pulses. This reveals the physical embodiments of concepts in knot theory, such as connected sums of knots and band surgeries. Our findings demonstrate the interplay of chirality effects at hierarchical levels from constituent molecules to the host medium and the energetically stable chiral vortex knots. This emergent physical behaviour may enable applications in electro-optics and photonics where such fusion and fission processes of vortex knots can be used for controlling light, as well as in spintronics when counterparts of such topological objects can be realized in the solid-state magnets.