Topological edge flows drive macroscopic reorganization in magnetic colloids

Magnetic colloids can be driven with time-varying fields to form clusters and voids that re-organize over vastly different timescales. However, the driving force behind these nonequilibrium dynamics is not well-understood. Here, we introduce a topological framework that predicts protected edge flows despite strong thermal motion. Notably, these edge flows produce shear stress that creates global rotation of clusters but not of voids. We verify this theory experimentally using micrometer-sized superparamagnetic colloids to demonstrate these emergent physical predictions and show how they drive system reorganization differentially at long timescales. Our results elucidate fundamental principles that shape and control nonequilibrium colloidal aggregates.