Distinguishing Ohmic and ballistic magnetrotransport around a circular barrier in graphene using scanning tunneling potentiometry

Efforts to directly image the microscopic physics involved in the quantum Hall effect – and magnetotransport in general – require probes capable of measuring voltages and currents far beyond the resolution of typical edge contacts, ideally at the nanometer scale. In this work, we use scanning tunneling potentiometry (STP) to spatially map the bulk Hall potential drop in ultraclean graphene/hBN samples with nanometer spatial and 100 microvolt energy resolution. In addition to measuring the bare Hall potential drop in the presence of weak, intrinsic disorder, we also image carrier flow around a circular electrostatic barrier ‘drawn’ with an STM tip. As the magnetic field is increased from 0 to 1.4 Tesla, we observe an Ohmic-to-ballistic transition in which the guiding center cyclotron motion along equipotential lines begins to dominate over diffusive motion. The Ohmic regime is characterized by a spiral pattern in the measured Hall potential, while the ballistic regime is marked by the appearance of two disk-like features centered around the electrostatic barrier. The disk-like features can only be reproduced at the level of the Boltzmann equation, which shows that the difference in their radii corresponds to the cyclotron diameter.