Simultaneous Imaging of the Electrostatic Potential and Current Density of Flowing Electrons in Two-dimensional Systems

Electronic transport in nanoscale devices is often characterized by a complex and non-local relation between electrostatic potential and current flow. Various techniques have been developed over the years for probing this relation, ranging from conventional transport measurements to scanning probe techniques sensitive to either potentials inside the samples or to local current density. However, none of the existing techniques provide a way to simultaneously map both the local electrostatic field and the current density in a non-invasive manner, on samples characterized by ballistic transport and in varying temperatures. In this work, we show a scanning technique for probing low dimensional nanoscale devices that achieves these goals. We demonstrate maps of both the local electrostatic potential due to current flow with 2μV/√Hz sensitivity and with a resolution of 150nm, as well as concurrent maps of the local current density by utilizing the relation between Hall voltage and current. This technique provides a tool for both basic measurements of the flow of electrons in complex quantum and interaction-dominated regimes, as well as for numerous practical applications.