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

Area of Science:

• Soft Matter Physics
• Condensed Matter Physics
• Materials Science

Background:

• Two-dimensional liquid crystals are characterized by quasi-long-ranged order.
• At equilibrium, orientational order parameter correlations decay as a power law: |r|^{-η_{p}}.
• The Berezinskii-Kosterlitz-Thouless transition universally sets η_{p}=1/4, signifying order loss due to disclination unbinding.

Purpose of the Study:

• To investigate the nature of quasi-long-ranged order in active liquid crystals.
• To determine if the established equilibrium framework for orientational order exponents applies to active systems.
• To explore the range of possible values for the order parameter exponent in active liquid crystals.

Main Methods:

• Theoretical analysis of active liquid crystal systems.
• Mathematical modeling of orientational order parameter correlations.
• Comparison of theoretical predictions with experimental data from various 2D active liquid crystal realizations.

Main Results:

• Quasi-long-ranged order in active liquid crystals fundamentally differs from equilibrium systems.
• The order parameter exponent, η_{p}, is not universally fixed but can vary.
• The exponent η_{p} is shown to be allowed in the range 0 < η_{p} ≤ 2, with the upper bound representing the isotropic phase.

Conclusions:

• The established understanding of quasi-long-ranged order in 2D liquid crystals needs revision for active systems.
• Active liquid crystals exhibit a broader and more flexible range of orientational order exponents.
• Theoretical predictions align with experimental observations across diverse 2D active liquid crystal systems.