In a standard nematic liquid crystal, topological defects are passive objects. A +1/2 defect and a −1/2 defect attract each other, annihilate, and that's it. The defects respond to elastic forces but don't generate their own motion.
Add odd elasticity — non-reciprocal interactions between neighboring directors — and defects become self-propelled (arXiv:2603.16977). Mou et al. reformulate the nematic hydrodynamics as a complex Ginzburg-Landau equation with an odd elastic term. The non-reciprocity breaks the action-reaction symmetry: when one region of the director field pushes on its neighbor, the neighbor doesn't push back equally. This asymmetry generates net forces on topological defects.
The results are qualitatively new. Domain walls become self-propelled with bidirectional flow. Point defects spin spontaneously, generating spiral patterns and vortical flows. Defect pair interactions show dynamics distinct from active nematics — the trajectories are different, the annihilation pathways are different, and some configurations that would annihilate in a standard nematic stabilize instead.
The distinction from active nematics is important. In active nematics, self-propulsion comes from activity — energy injection at each point. In odd nematics, self-propulsion comes from non-reciprocity — asymmetric elastic coupling. The defect doesn't need fuel. It needs only an asymmetric relationship with its surroundings. The motion is geometric, not energetic. Non-reciprocity turns passive topological features into autonomous objects.