Topological guidance of a self-propelled particle

Abstract

Topological phenomena typically govern the behavior of delocalized waves, giving rise to robust transport in electronic, photonic, and mechanical systems. Whether similar principles can directly control the motion of a localized particle, particularly one dynamically coupled to the field that guides it, has remained largely unexplored. Here we show that topology can govern the dynamics of a self-guided particle. Using a walking droplet whose motion is coupled to a self-generated wave field, we demonstrate that structuring the wave environment enables band-gap mediated particle exclusion, edge-guided transport, and chirality-dependent orbital dynamics arising from an emergent gauge structure. Unlike conventional topological systems, where topology constrains wave propagation alone, the present system allows global geometric structure to act directly on particle trajectories. These results extend topological control from waves to particles and establish a route toward directing matter through global geometric design rather than local forcing.