Scanned potential microscopy of edge states in a quantum Hall liquid

Using a low-temperature atomic force microscope as a local voltmeter, we measure the Hall voltage profile in a quantum Hall conductor in the presence of a gate-induced non-equilibrium edge state population at ν=3. We observe sharp voltage drops at the sample edges which are suppressed by re-equilibrating the edge states. The system studied is a GaAs/AlGaAs heterostructure with a two-dimensional electron system lying 90 nm below the surface. This work highlights the previously unobservable local properties of the quantum Hall liquid, presenting measurements of the electrostatic potential at the quantum Hall liquid's edge. The results demonstrate the influence of edge states on the transport properties of the quantum Hall conductor and expand upon existing experimental techniques by utilizing scanned probe technologies. These findings pave the way for further investigations into the behavior of edge states under various conditions and contribute to our understanding of quantum Hall systems, which have critical implications in condensed matter physics.