The advent of ultra-clean materials in recent years has enabled the exploration of previously inaccessible electron flow regimes, including ballistic flow, where electrons traverse a sample unperturbed before colliding with the walls, as well as hydrodynamic flow, where strong electron-electron interactions may lead to electrons flowing like a conventional fluid. These flow phenomena are predicted to exhibit a rich set of spatial voltage and current patterns, which to date have eluded observation.
We have developed a nanoscale probe that is ideally suited for imaging such electron flow based on a scanning nanotube single electron transistor. Our technique is capable of simultaneously imaging voltage and current distributions with high sensitivity and minimal invasiveness, in magnetic field, across a broad range of temperatures, and below insulating surfaces. Applying our technique to high-mobility graphene devices, we observe the evolution from ohmic flow, in which the electrostatic potential of the flowing electrons drops gradually across the device, into ballistic flow, where it drops sharply at the contacts. We further map the negative voltage distribution of ballistic flow, demonstrating the ability to image intrinsically non-local flow patterns that are hidden in a typical transport measurement. Finally, we image flow through graphene channels and visualize for the first time the emergence of parabolic, Poiseuille current profiles of hydrodynamic electrons. Our results provide long-sought, direct confirmation of elementary physical particles flowing hydrodynamically, and enable the further exploration of the rich physics of interacting electrons in real space.