Disorder and Integral Quantum Hall Effect

TL;DR

This paper demonstrates that in a disordered 2D electron gas, the quantum Hall conductance remains quantized and unaffected by disorder, with no localized states, emphasizing the role of energy gaps in Hall plateaus.

Contribution

It shows that disorder does not destroy the quantized Hall conductance in the absence of Landau level mixing, highlighting the persistence of current-carrying states.

Findings

Hall conductance remains quantized despite disorder

No localized states are present in the system

Hall plateaus require an energy gap between broadened Landau levels

Abstract

The quantum Hall conductance of a disordered two-dimensional gas of non-interacting electrons is re-examined for its integrity against disorder in the limit of no mixing between different Landau levels. The exact one-electron eigenstates of the disordered system are shown to be current carrying, with exactly the same Hall current as in the absence of disorder. There are no localized states. Accordingly, each extensively degenerate Landau level, now broadened out by the disorder, continues to contribute exactly one quantum of Hall conductance ($e^2/2\pi\hbar$). In the absence of any localized (non-current carrying) states, the Hall plateaus can now arise only through an actual gap in the density of states separating the broadened Landau levels. Implications for 2D localization are discussed.