Quantum Hall effect in a high-mobility two-dimensional electron gas on the surface of a cylinder

TL;DR

This study explores the quantum Hall effect in a high-mobility two-dimensional electron gas on a cylindrical surface, revealing inhomogeneous current distributions and resistance asymmetries due to the novel topology.

Contribution

It introduces a self-consistent model incorporating screening theory and the static skin effect to explain experimental observations in a cylindrical quantum Hall system.

Findings

Resistance asymmetry relations hold beyond integer filling factors

Model explains inhomogeneous current distribution and resistance features

System exhibits metallic behavior due to incompressible-compressible transition

Abstract

The quantum Hall effect is investigated in a high-mobility two-dimensional electron gas on the surface of a cylinder. The novel topology leads to a spatially varying filling factor along the current path. The resulting inhomogeneous current-density distribution gives rise to additional features in the magneto-transport, such as resistance asymmetry and modified longitudinal resistances. We experimentally demonstrate that the asymmetry relations satisfied in the integer filling factor regime are valid also in the transition regime to non-integer filling factors, thereby suggesting a more general form of these asymmetry relations. A model is developed based on the screening theory of the integer quantum Hall effect that allows the self-consistent calculation of the local electron density and thereby the local current density including the current along incompressible stripes. The model, which also includes the so-called `static skin effect' to account for the current density distribution in the compressible regions, is capable of explaining the main experimental observations. Due to the existence of an incompressible-compressible transition in the bulk, the system behaves always metal-like in contrast to the conventional Landauer-Buettiker description, in which the bulk remains completely insulating throughout the quantized Hall plateau regime.