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

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.

arXiv comment20 pages, 9 figures

References in corpus (10)

• A New Transport Regime in the Quantum Hall Effect
• The Quantized Hall Insulator: A New Insulator in Two-Dimensions
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• Does theory of quantum correction to conductivity agree with experimental data in 2D systems?
• Non-Universal Behavior of Finite Quantum Hall Systems as a Result of Weak Macroscopic Inhomogeneities
• The Nature of the Hall Insulator
• (Mis-)handling gauge invariance in the theory of the quantum Hall effect III: The instanton vacuum and chiral edge physics
• Establishing a non-Fermi liquid theory for disordered metals near two dimensions
• Evidence for a Quantum Hall Insulator in an InGaAs/InP Heterostructure
• Universality at integer quantum Hall transitions

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• Quantum criticality, particle-hole symmetry, and duality of the plateau-insulator transition in the quantum Hall regime
• Quantum critical behaviour of the plateau-insulator transition in the quantum Hall regime
• Tuning of quantum interference in top-gated graphene on SiC
• Observation of the quantized Hall insulator in the quantum critical regime of the two-dimensional electron gas
• Magnetic field dependent equilibration of fractional quantum Hall edge modes