Origin of Edge Currents in Chiral Active Liquids

Chiral active liquids generically exhibit unidirectional edge currents in confinement. While this phenomenon has been attributed to model-specific mechanisms and interpreted through phenomenological equations, a universal understanding of it, and its connection to microscopic dynamics remain absent. Starting from the microscopic equations of motion of a simple interacting two-dimensional model, we find that localized edge currents emerge as a consequence of global angular momentum balance. 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. This origin of the edge current is shown to extend to other models of chiral systems where angular momentum is injected in distinct ways.