The effects of macroscopic inhomogeneities on the magneto transport properties of the electron gas in two dimensions

TL;DR

This paper develops a formalism to account for macroscopic inhomogeneities in two-dimensional electron gas experiments, revealing their impact on magneto-transport measurements and the interpretation of quantum Hall transitions.

Contribution

It introduces a general formalism for sample inhomogeneities affecting magneto resistance data, and analyzes their influence on different transport regimes and quantum Hall transition interpretations.

Findings

Inhomogeneities significantly affect plateau-plateau transition measurements.

A universal scaling law for magneto resistance parameters is proposed.

Weak-field semiclassical regime is crucial for understanding quantum Hall experiments.

Abstract

In experiments on electron transport the macroscopic inhomogeneities in the sample play a fundamental role. In this paper and a subsequent one we introduce and develop a general formalism that captures the principal features of sample inhomogeneities (density gradients, contact misalignments) in the magneto resistance data taken from low mobility heterostructures. We present detailed assessments and experimental investigations of the different regimes of physical interest, notably the regime of semiclassical transport at weak magnetic fields, the plateau-plateau transitions as well as the plateau-insulator transition that generally occurs at much stronger values of the external field only. It is shown that the semiclassical regime at weak fields plays an integral role in the general understanding of the experiments on the quantum Hall regime. The results of this paper clearly indicate that the plateau-plateau transitions, unlike the the plateau-insulator transition, are fundamentally affected by the presence of sample inhomogeneities. We propose a universal scaling result for the magneto resistance parameters. This result facilitates, amongst many other things, a detailed understanding of the difficulties associated with the experimental methodology of H.P. Wei et.al in extracting the quantum critical behavior of the electron gas from the transport measurements conducted on the plateau-plateau transitions.