Chiral Edge Modes in Helmholtz-Onsager Vortex Systems

Vortices play a fundamental role in the physics of 2 dimensional (2d) fluids across a range of length scales, from quantum superfluids to geophysical flows. Despite a history dating back to Helmholtz, the study of point vortices in a classical 2d fluid continues to be of interest, owing to their unusual statistical mechanics. Recent experiments show that this model confirms the phenomenon of vortex condensation in superfluids. However, the effects of boundary geometry in the subcritical energy regime have not yet been explored in detail. Here we show that confined Helmholtz-Onsager systems contain edge modes at subcritical energy, extending a previously identified analogy between vortex matter and quantum Hall systems. Through numerical simulations and mean field models, we demonstrate that angular momentum conservation in a disk leads to a symmetry protected edge mode. These edge modes are robust, persisting in nonconvex domains. Furthermore, using analytics and numerical simulations, we exhibit a subcritical phase separation associated with edge modes in neutral Helmholtz-Onsager systems at finite particle number.