Spontaneous generation of angular momentum in chiral active crystals

TL;DR

This paper demonstrates that chiral active particles in a two-dimensional crystal spontaneously generate angular momentum and exhibit unique dynamic behaviors due to chirality, with implications for understanding active matter systems.

Contribution

It provides an analytical and numerical study of how chirality induces angular momentum and alters fluctuation spectra in active crystals, a novel insight into chiral active matter.

Findings

Chirality reduces displacement and velocity fluctuations.

Chirality induces net angular momentum with non-monotonic dependence on chirality degree.

Chirality causes a non-dispersive peak in the displacement spectrum.

Abstract

We study a two-dimensional chiral active crystal composed of underdamped chiral active particles. These particles, characterized by intrinsic handedness and persistence, interact via linear forces derived from harmonic potentials. Chirality plays a pivotal role in shaping the system's behavior: it reduces displacement and velocity fluctuations while inducing cross-spatial correlations among different Cartesian components of velocity. These features distinguish chiral crystals from their non-chiral counterparts, leading to the emergence of net angular momentum, as predicted analytically. This angular momentum, driven by the torque generated by the chiral active force, exhibits a non-monotonic dependence on the degree of chirality. Additionally, it contributes to the entropy production rate, as revealed through a path-integral analysis. We investigate the dynamic properties of the crystal in both Fourier and real space. Chirality induces a non-dispersive peak in the displacement spectrum, which underlies the generation of angular momentum and oscillations in time-dependent autocorrelation functions or mean-square displacement, all of which are analytically predicted.