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. We show that the system in the fluid phase crystallizes at high densities even in two dimensions. The true long-range translational order arises due to the suppression of displacement fluctuations associated with hyperuniformity. We also find that Ω=0 is singular, where the system never crystallizes because the system is similar to a quenched random system for which the lower critical dimension is $4$. Our numerical results are quantitatively explained by a linear elastic theory.