A simple microscopic description of quantum Hall transition without Landau levels

TL;DR

This paper presents a microscopic model of the quantum Hall transition that occurs without Landau levels, using a network of channels to analyze the effects of backscattering and magnetic bending on electron transport.

Contribution

It introduces a simplified network model capturing the quantum Hall transition without relying on Landau levels, highlighting the roles of backscattering and magnetic bending.

Findings

Quantum Hall transition occurs without Landau levels.

Backscattering limits electron mobility.

Magnetic bending induces Hall conductivity quantization.

Abstract

By restricting the motion of high-mobility 2D electron gas to a network of channels with smooth confinement, we were able to trace, both classically and quantum-mechanically, the interplay of backscattering, and of the bending action of a weak magnetic field. Backscattering limits the mobility, while bending initiates quantization of the Hall conductivity. We demonstrate that, in restricted geometry, electron motion reduces to two Chalker-Coddington networks, with opposite directions of propagation along the links, which are weakly coupled by disorder. Interplay of backscattering and bending results in the quantum Hall transition in a non-quantizing magnetic field, which decreases with increasing mobility. This is in accord with scenario of floating up delocalized states.