Origin of Edge Currents in Chiral Active Liquids

Abstract

Chiral active liquids exhibit unidirectional edge currents when confined to simple geometries, but the origin of this phenomenon has defied explanation. Starting from the microscopic equations of motion of a simple two-dimensional model, we find that localized edge currents emerge as a consequence of global angular momentum conservation in dense systems. From these underlying equations, we derive an Ohmic-like conductance law for the mean edge current in the dense phase, and we find it to be intensive, depending only on the density, active torque and substrate drag. For simple geometries, we find the distribution of the edge currents has a closed Gaussian form, with a variance that is intensive, depending only on temperature, density and the aspect ratio of the system. These results are validated numerically using extensive molecular dynamics simulations. These results provide a new perspective for studying the collective phenomena in active matter through the global balance of conserved quantities.

Figures (3)

• Figure 1: (a) Universality of edge currents. The unidirectional edge current persists over obstacles. The color scale shows the scaled absolute value of the averaged velocity field. Black solid lines represent the walls. Localized velocity profiles for the parallel-plate, $L_x=2L_y=300\sigma$ (b) and circular, $R=100 \sigma$ (c) geometries for $\tau_a=2.5 \epsilon$, $\rho=0.8 m\sigma^{-2}$ and $\gamma=0.1\sqrt{m\epsilon\sigma^{-2}}$. Dashed lines are the hydrodynamic profiles.
• Figure 2: Statistics of the total angular momentum density. (a) The autocorrelation function of the total angular momentum density in the circular confinement. (b) Distribution of the angular momentum density. Dashed lines are the theoretical predictions.
• Figure 3: Edge current as a function of active torque for parallel-plate, $L_x=L_y=400\sigma$ (a) and circular, $R=250\sigma$ (b) geometries at different densities and drag coefficients. The dashed lines are the predictions from the balance of angular momentum. (c) Steady-state edge current distribution for the parallel-plate confinement for different parameters.