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 two-dimensional 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. In addition, 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 current in the QH regime.