Scanned Potential Microscopy of Edge and Bulk Currents in the Quantum Hall Regime

Using an atomic force microscope as a local voltmeter, we measure the Hall voltage profile in a 2D electron gas in the quantum Hall (QH) regime. We observe a linear profile in the bulk of the sample in the transition regions between QH plateaus and a distinctly nonlinear profile on the plateaus. Additionally, localized voltage drops are observed at the sample edges in the transition regions. We interpret these results in terms of theories of edge and bulk currents in the QH regime. The universal nature of the quantization in QH conductors suggests resistance characteristics that are independent of microscopic properties, thus making local current and voltage distributions within the sample inaccessible with standard transport measurements. This study addresses ongoing controversies regarding the localization of current flow and associated voltage drops, with some theories proposing edge concentration of current while others predict bulk distribution. Our findings, highlighting discrepancies between measured Hall voltages on QH plateaus and transition regions, provide insight into potential non-equilibrium current flow in edge states.