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

We numerically study two-dimensional athermal chiral active particles at high densities. The particles in this system perform the circular motion with frequency Ω. The system is known to undergo a nonequilibrium transition from the absorbing phase to the diffusing fluid phase that is accompanied by the suppression of density fluctuations called hyperuniformity [Q.-L. Lei et al., Sci. Adv. 5, eaau7423 (2019)]. We show that the system in the fluid phase crystallizes with increasing density. Surprisingly, the resulting crystal possesses long-range translational order even in two dimensions due to the suppression of the long-wavelength displacement fluctuations associated with hyperuniformity. We also find that Ω = 0 is singular, and the system never crystallizes because, in this limit, the system can be regarded as a quenched random system for which the lower critical dimension is known to be 4. Our numerical results are quantitatively explained by a linear elastic theory.