Motile dislocations knead odd crystals into whorls

The competition between thermal fluctuations and potential forces governs the stability of matter in equilibrium, in particular the proliferation and annihilation of topological defects. However, driving matter out of equilibrium allows for a new class of forces which are neither attractive nor repulsive, but rather transverse. The possibility of activating transverse forces raises the question of how they affect basic principles of material selforganization and control. Here, we show that transverse forces organize colloidal spinners into odd elastic crystals crisscrossed by motile dislocations. These motile topological defects organize into a poly-crystal made of grains with tunable length scale and rotation rate. The self-kneading dynamics drive super-diffusive mass transport, which can be controlled over orders of magnitude by varying the spinning rate. Simulations of both a minimal model and fully resolved hydrodynamics establish the generic nature of this crystalwhorl state.