Classical versus Quantum Transport near Quantum Hall Transitions

TL;DR

This paper compares classical and quantum transport mechanisms near quantum Hall transitions, clarifying experimental discrepancies by identifying distinct conduction regimes and their temperature-dependent behaviors.

Contribution

It introduces a framework distinguishing classical and quantum transport regimes near quantum Hall transitions, explaining experimental results through their different temperature dependencies.

Findings

Classical regime shows activated resistivity and quantized Hall insulator behavior.

Quantum regime exhibits variable range hopping with different temperature dependence.

A crossover between regimes occurs at low temperatures or far from the critical point.

Abstract

In attempt to settle the apparent disagreements between different experimental results, transport data near quantum Hall transitions are interpreted by identifying two distinct conduction regimes. The ``classical'' regime, dominated by nearest neighbor hopping between localized conducting puddles, manifests an activated-like resistivity formula, and the quantized Hall insulator behavior. At very low temperatures $T$, or farther from the critical point, a crossover occurs to a "quantum" transport regime dominated by variable range hopping. The latter is characterized by a different T-dependence, yet the dependence on filling fraction is, coincidentally, hard to distinguish.