Spatial imaging of electron flow in Corbino geometry

Electron flow is classified into three distinct transport regimes: diffusive, ballistic and hydrodynamic. Each regime exhibits a unique spatial profile for the potential of flowing electrons. The Corbino disk geometry, in which current is driven from a circular central contact to an outer ring, ideally highlights the differences between these spatial flow profiles. Unlike a channel geometry, the Corbino disk has no edges between the source and drain electrodes, and therefore electrons can only transfer momentum to impurities, phonons, or other electrons. Amazingly, in the hydrodynamic regime - which is dominated by momentum conserving electron-electron interactions- the electric field is predicted to be expelled entirely from the bulk of the disk leading to a spatially flat electrostatic potential, resulting in a lower resistance than the fully ballistic regime. Here, we present our results on imaging the potential profiles in different transport regimes in a graphene Corbino disk. Using a scanning nanotube single-electron transistor as an ultrasensitive charge detector, we spatially image the potential of flowing electrons in corbino disk. By varying the carrier density and temperature, the imaged potential profiles clearly distinguish the different transport regimes.