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

TL;DR

This paper introduces a new representation of bulk current in the quantum Hall effect regime, linking network models with tunneling processes and phase coexistence, enhancing understanding of plateau transitions.

Contribution

It demonstrates the equivalence of a Landauer-Buttiker network approach with tunneling models and maps phase coexistence to a checkerboard pattern, revealing the role of droplet size in plateau sharpness.

Findings

Network representation aligns with tunneling process models.

Phase coexistence involves coupled droplets of QH liquid and insulator.

Plateau transition sharpness depends on droplet size and disorder.

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.