Current vortices in ballistic transport: Collective motion <i>without</i> interactions

Diffusive transport breaks down when the mean free path due to momentum-relaxing scattering (e.g., electron-phonon, electron-defect) exceeds the device-scale, as is now routine in two-dimensional systems. The ballistic transport regime then occurs when momentum-conserving scattering (e.g., normal electron-electron) is also sufficiently weak: carriers propagate along ballistic trajectories, while only being scattered off the device boundaries. In contrast, the hydrodynamic transport regime occurs when momentum-conserving scattering dominates, wherein the carriers move collectively like in a fluid. Both regimes can occur in the same device (at distinct temperatures), and have very different conceptual underpinnings. The ballistic regime exemplifies single-particle intuition, whereas the hydrodynamic regime is prototypical of collective phenomenon. The latter is most easily visualized in current vortices: flow patterns formed by the collection of all individual carrier trajectories. We show that, despite no interactions, the ballistic regime also gives rise to vortices. The ballistic vortices are distinct from those in the hydrodynamic regime, and depend on the shape of the Fermi surface. We showcase the striking patterns formed by circular and hexagonal Fermi surfaces.