Singular density correlations in chiral active fluids in three dimensions

We investigate density fluctuations in three-dimensional chiral active fluids by using a simple model of helical self-propelled particles. Helical motion is generated by a constant angular velocity (or chiral torque) acting on the self-propelled force. The chiral torque is assumed to have the same direction and magnitude for all particles. Due to the helical nature of the particle motion, the system is generically anisotropic even when it is spatially homogeneous. Numerical simulations demonstrate that the helicity induces an anisotropic pattern and a singularity in the static structure factor (the density correlation function in Fourier space) in the low-wave-number limit. Moreover, the system in the limit of infinite persistence time exhibits hyperuniformity in the direction perpendicular to the chiral torque, while giant density fluctuations emerge along the parallel direction. We then construct a fluctuating hydrodynamic theory for the system to describe the singular behavior. A linear analysis of the resulting equations yields an analytical expression for the static structure factor, which qualitatively agrees with our numerical findings.