Current distribution and Hall potential landscape towards breakdown of the quantum Hall effect: a scanning force microscopy investigation

We present line- and area-scans of the Hall potential landscape of a two-dimensional electron system (2DES) in narrow (AlGa) As-based Hall bars under quantum Hall (QH) conditions, obtained by low-temperature scanning force microscopy. For several magnetic field values B in the regime of the QH plateau with Landau level filling factor nu = 2, we measured the evolution of the Hall potential profiles and of the longitudinal voltage drop along the Hall bar as a function of increasing voltage/current bias, leading finally to the electrically induced breakdown of the quantum Hall effect (QHE). Basically two types of evolution were observed: for the low B-field side of the QHE plateau, two distinct Hall potential drops appear close to the two edges of a cross section, equally distributed at low bias but continuously developing to an asymmetrical distribution with increasing bias. At high bias, a steady increase of the longitudinal voltage drop is observed, accompanied by a rising slope of the Hall potential drop in the bulk. For the upper B-field side of the QH plateau, the Hall voltage drops are broadly distributed across the whole cross section, and the distribution remains almost unchanged until the bias reaches a critical value where the Hall potential profile changes rather abruptly, enhancing locally the Hall field. Beyond this, with further increase of the bias, a steep rise of the longitudinal voltage drop is detected. These findings are naturally explained in the microscopic picture of the QHE, based on the self-consistent evolution of the compressible and incompressible landscape inside the 2DES with increasing bias.