Defect unbinding in active nematics

TL;DR

This paper develops a theoretical framework for understanding how active forces influence the unbinding of topological defects in two-dimensional active nematic systems, revealing a phase diagram with re-entrant transitions and activity-dependent defect stability.

Contribution

It derives an interacting particle model including active torques from hydrodynamics, showing how activity lowers the defect unbinding temperature and introduces a critical activity threshold.

Findings

Activity lowers the defect unbinding transition temperature.

A critical activity separates ordered and disordered phases.

Re-entrant transition occurs at low temperatures with increasing activity.

Abstract

We formulate the statistical dynamics of topological defects in the active nematic phase, formed in two dimensions by a collection of self-driven particles on a substrate. An important consequence of the non-equilibrium drive is the spontaneous motility of strength +1/2 disclinations. Starting from the hydrodynamic equations of active nematics, we derive an interacting particle description of defects that includes active torques. We show that activity, within perturbation theory, lowers the defect-unbinding transition temperature, determining a critical line in the temperature-activity plane that separates the quasi-long-range ordered (nematic) and disordered (isotropic) phases. Below a critical activity, defects remain bound as rotational noise decorrelates the directed dynamics of +1/2 defects, stabilizing the quasi-long-range ordered nematic state. This activity threshold vanishes at low temperature, leading to a re-entrant transition. At large enough activity, active forces always exceed thermal ones and the perturbative result fails, suggesting that in this regime activity will always disorder the system. Crucially, rotational diffusion being a two-dimensional phenomenon, defect unbinding cannot be described by a simplified one-dimensional model.