Visualizing unexpected magnetic field-tuned electron flow through ballistic channels

The advent of ultra-clean materials has enabled the exploration of ballistic flow, where electrons traverse a sample unperturbed before colliding with the walls. We have developed a nanoscale probe based on a scanning nanotube single electron transitor that is sufficiently sensitive to image the electrostatic potential of ballistic electrons in such materials for the first time. We apply this probe to high-mobility graphene channel devices, and image how the potential of the flowing electrons drops sharply at the contacts while remaining constant along the bulk, which is the textbook picture of ballistic electron flow. We then image how the Hall voltage profiles of the flowing electrons develop a rich set of patterns as the cyclotron radius is tuned by varying the perpendicular magnetic field. Contrary to the expectation that the electron current primarily flows along the edges in magnetic field, our results reveal that the current varies considerably across the bulk of the channel, and can even concentrate near the center. These results open the path for visualizing other ballistic electron flow phenomena that previously could only be studied via transport, including electron optics.