Defect unbinding and a motile Kosterlitz-Thouless transition in active nematics*

Active nematic liquid crystals formed by a collection of self-driven particles on a two-dimensional substrate exhibit complex spatio-temporal dynamics and spontaneous defect proliferation. An important consequence of the non-equilibrium drive is the spontaneous motility of strength +1/2 disclinations that drives flow in the system. Starting from the hydrodynamic equations of active nematics, we derive effective equations for the topological defects as interacting overdamped particles with pair forces and active torques. Using these equations we then show that activity lowers the defect-unbinding transition temperature driving a nonequilibrium variant of the Kosterlitz-Thouless transition into a state of defect chaos. Crucially, we find rotational noise stabilizes nematic order at low activity leading to a re-entrant transition. For large activity, orientational torques on the defects combined with many-body screening allows the spontaneous appearance of a polar defect ordered liquid, rationalizing previous work into a comprehensive phase diagram for two-dimensional active nematics.