Quasi-Long-Ranged Order in Two-Dimensional Active Liquid Crystals

Quasi-long-ranged order is the hallmark of two-dimensional liquid crystals. At equilibrium, this property implies that the correlation function of the local orientational order parameter decays with distance as a power law: i.e., ∼|r|^{-η_{p}}, with η_{p} a temperature-dependent exponent. While in general nonuniversal, η_{p}=1/4 universally at the Berezinskii-Kosterlitz-Thouless transition, where orientational order is lost because of the unbinding of disclinations. Here, we demonstrate that, in active liquid crystals, the notion of quasi-long-ranged order fundamentally differs from its equilibrium counterpart, and the exponent η_{p} is allowed to vary in the range 0<η_{p}≤2, with the upper bound corresponding to the isotropic phase. Our theoretical predictions are supported by a survey of a variety of experimental realizations of two-dimensional active liquid crystals.