Imaging ballistic and hydrodynamic electron flow in the Corbino geometry

Hydrodynamic flow is predicted to exhibit unique voltage patterns which are distinct from both the Ohmic and ballistic regimes. A flow geometry to best highlight these patterns is the Corbino disc, in which the current is driven from a circular central contact into an outer ring. In this geometry there are no walls, and so the electrons can only transfer momentum to either impurities or to other electrons. In the hydrodynamic regime in which the flow is dominated by such electron-electron scattering, momentum is conserved, leading to an expulsion of the electric field across the bulk of the disc and hence a constant electrostatic potential. In this situation, the device resistance may even be lower than in the fully ballistic regime, where the potential drops inversely with the radius. We present our initial results on imaging electron flow in high-mobility graphene Corbino discs using a nanotube single electron transistor. We image the voltage drop of the flowing electrons from the inner to outer contact, with the aim of distinguishing these unique spatial signatures of ballistic and hydrodyanmic flow.