Abstract
Asymmetry is essential for function-from the chiral molecules of life to the directed motion of micromachines. Yet encoding persistent asymmetries into the dynamics of synthetic systems typically requires time-varying external fields or complex feedback mechanisms. Here, we show that static geometry alone can program asymmetric colloidal motion by exploiting topological defects in liquid crystals. By simply translating one patterned substrate relative to another, we transform circular disclination loops into eccentric ellipses, breaking rotational symmetry and generating distinct topological profiles along the loop's upper and lower segments. Colloidal particles threaded onto these reconfigured loops exhibit striking asymmetry: they undergo opposing rotations on topologically distinct halves, with a fixed difference in rotation numbers that originates from a geometric phase shift-a phase shift that can be precisely manipulated through pattern design. We generalize this framework to demonstrate that non-equilibrium light-driven dynamics amplify these asymmetries, enabling colloidal micromachines whose rotational trajectories are embedded in the static geometry of the host material. Our work establishes topological defect engineering as a paradigm for programming asymmetry in soft materials, with implications for microrobotics, active matter, and autonomous material systems.