A new representation of the bulk current in the quantum Hall effect regime

Abstract

In preceding papers a Landauer-Buttiker type representation of bulk current transport has been successfully used for the numerical simulation of the magneto transport of 2-dimensional electron systems in the high magnetic field regime. In this paper it is demonstrated, that this representation is in full agreement with a treatment of the bulk current transport as a tunneling process between magnetic bound states. Additionally we find a correspondence between our network representation and the bulk current picture in terms of mixed phases mapped on a checkerboard: At half filled Landau level (LL) coupled droplets of a quantum Hall (QH) liquid phase and coupled droplets of an insulator phase phase exist at the same time, with each of them occupying half of the sample area. Removing a single electron from to such a QH liquid droplet at half filling completes the QH transition to the next higher QH plateau. Adding a single electron to such a droplet at half filling completes the QH transition to the previous lower QH plateau. As a consequence, the sharpness of the QH plateau transitions on the magnetic field axis depends on the typical size of the droplets, which can be understood as a measure of the disorder in the sample.