Quantum Hall effect at low magnetic fields

TL;DR

This paper clarifies that low-field quantum Hall effects observed experimentally align with standard scaling theory, attributing apparent discrepancies to weak localization and Landau quantization effects.

Contribution

It demonstrates that recent experimental claims of deviation from the global phase diagram are consistent with established theory, explaining low-field transitions as crossover phenomena.

Findings

Experimental results agree with standard scaling theory.

Low-field transition is due to weak localization and Landau quantization.

No fundamental discrepancy with the quantum Hall phase diagram.

Abstract

The temperature and scale dependence of resistivities in the standard scaling theory of the integer quantum Hall effect is discussed. It is shown that recent experiments, claiming to observe a discrepancy with the global phase diagram of the quantum Hall effect, are in fact in agreement with the standard theory. The apparent low-field transition observed in the experiments is identified as a crossover due to weak localization and a strong reduction of the conductivity when Landau quantization becomes dominant.