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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi mathvariant="normal">Ω</a:mi></a:math>. 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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi mathvariant="normal">Ω</c:mi><c:mo>=</c:mo><c:mn>0</c:mn></c:mrow></c:math>, 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.