Topology of pulsating active matter: Defect asymmetry controls emergent motility

In pulsating active matter, topological defects are motile despite the absence of any macroscopic flows and microscopic self-propulsion. We reveal that this motility arises from a ratchet effect: the mechanochemical coupling between local oscillations and repulsive interactions breaks both spatial and time-reversal symmetries, thus leading asymmetric rotating defects to drift under fluctuations. This mechanism regulates a crossover between spiral waves connecting slow defects and fiber-like waves connecting fast defects, in analogy with the onset of heart rhythm disorder in cardiac tissues. We rationalize this crossover in terms of a fluctuating hydrodynamics that captures how motile defects spontaneously nucleate and move within an ordered background.