A sweeping twist defect as a topological flagellum that drives colloid motion

Nematic liquid crystals can dramatically reconfigure under dynamic forcing, providing exciting opportunities in active matter. Here, we study a hybrid disk colloid rotated by an external field which generates a dynamic companion topological defect. The disk moves faster when the defect sweeps across the disk's face. We identify the defect as a non-singular twist wall, characterize the twist energy landscape, and identify the sweeping motion as a topological instability. As the defect sweeps, it reverses the handedness of twist and lowers the free energy in the fluid in the gap above the disk. Landau-de Gennes modeling shows that the sweeping wall behaves as a propagating director texture: the director field is nearly stationary in the wall frame, while nematogens rotate locally as the wall passes. The nematogens' rotation generates a viscous stress on the surface of the disk that hastens its propulsion. Thus, the defect acts as a flagellum that powers colloid swimming, providing an example of a dissipative topological structure whose dynamics can be harnessed to perform useful work.