Topological edge flows drive macroscopic re-organization 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 non-equilibrium 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 micron-sized super-paramagnetic colloids to demonstrate these emergent physical predictions and show how they drive system re-organization differentially at long timescales. Our results elucidate fundamental principles that shape and control non-equilibrium colloidal aggregates.