Long-range translational order and hyperuniformity in two-dimensional chiral active crystal

TL;DR

This study demonstrates that high-density two-dimensional chiral active particles form crystals with true long-range order and hyperuniformity, with stability depending on the particles' circular motion frequency.

Contribution

It reveals the emergence of long-range translational order and hyperuniformity in 2D chiral active particles, and explains the instability at zero frequency using active elastic theory.

Findings

Crystallization occurs at high densities with true long-range order.

Hyperuniformity suppresses displacement fluctuations.

Crystals melt at zero circular motion frequency in four or fewer dimensions.

Abstract

We numerically study two-dimensional athermal chiral active particles at high densities. The particles in this system perform the circular motion with frequency $\Omega$. We show that the system crystallizes at high densities even in two dimensions, accompanied by the true long-range translational order. This is due to the anomalous suppression of displacement fluctuations associated with hyperuniformity. These findings can be explained using an active elastic theory quantitatively. Surprisingly, the crystals become unstable and melt in the limit of $\Omega=0$, for the spatial dimension of four or less. This result can be explained by a mechanism akin to quenched random systems for which the lower critical dimension is four.