Imaging spatial structure of skipping orbits in ballistic magnetotransport through graphene

Graphene has emerged as the novel Van der Waals heterostructure for performing electron transport experiments. The ability to fabricate ultraclean devices with high electron mobility along with the tunability of the carrier density has made it an ideal material for studying ballistic electron transport. At low carrier densities, electrons in graphene obey ohmic transport, which is characterized by dominant bulk scattering and leads to a local relation between the current density and the electric field. This changes at high densities when the transport becomes ballistic and non-local. In this talk, I will present our non-invasive study of this crossover to non-local electron transport, imaged using a scanning single-electron transistor. Deep in the ballistic regime and under small non-quantizing perpendicular magnetic fields, we observe that the transverse electric field Ey shows a curious spatial structure. Specifically, we see that with increasing magnetic field, Ey measured in a rectangular channel develops a central cusp which splits into two peaks. Using electron billiards simulations, we show that these spatial structures reflect the internal structure of the semi-classical skipping orbits at the sample boundaries.