A simple microscopic description of quantum Hall transition without Landau levels

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.

Published version

References in corpus (4)

• Random Network Models and Quantum Phase Transitions in Two Dimensions
• The instanton vacuum of generalized $C{P}^{N-1}$ models
• Levitation of the quantum Hall extended states in the $B\to$ 0 limit
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Cited by in corpus (5)

• Random network models with variable disorder of geometry
• Anti-Levitation in the Integer Quantum Hall Systems
• Weakly chiral networks and 2D delocalized states in a weak magnetic field
• Phase diagram of weak-magnetic-field quantum Hall transition quantified from classical percolation
• Supersymmetry approach to delocalization transitions in a network model of the weak field quantum Hall effect and related models