Spontaneous generation of angular momentum in chiral active crystals.

We study a two-dimensional chiral active crystal composed of underdamped chiral active particles. These particles, characterized by intrinsic handedness and persistence, interact 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.