Widths of the Hall Conductance Plateaus

TL;DR

This paper analyzes the quantum Hall effect in disordered two-dimensional electron systems, proving the existence of localized states and demonstrating quantized Hall conductance plateaus as the filling factor varies.

Contribution

It provides a rigorous proof of localized states in disordered Landau bands and establishes the quantization of Hall conductance in the localization regime.

Findings

Existence of localized bulk states below a certain energy threshold.

Hall conductance remains quantized and forms plateaus when the Fermi level is in the localization regime.

Quantization depends on the filling factor, not the Fermi level.

Abstract

We study the charge transport of the noninteracting electron gas in a two-dimensional quantum Hall system with Anderson-type impurities at zero temperature. We prove that there exist localized states of the bulk order in the disordered-broadened Landau bands whose energies are smaller than a certain value determined by the strength of the uniform magnetic field. We also prove that, when the Fermi level lies in the localization regime, the Hall conductance is quantized to the desired integer and shows the plateau of the bulk order for varying the filling factor of the electrons rather than the Fermi level.