The quantized Hall effect in the presence of resistance fluctuations

TL;DR

This study demonstrates that in mesoscopic 2D electronic systems under high magnetic fields, the Hall resistivity remains quantized despite strong resistance fluctuations, confirming the semicircle law's applicability at small scales.

Contribution

It provides experimental evidence that the quantized Hall effect persists in mesoscopic systems with resistance fluctuations, extending the semicircle law to this regime.

Findings

Hall resistivity remains quantized despite fluctuations

Semicircle law holds in mesoscopic regime

Resistance fluctuations are sample-specific

Abstract

We present an experimental study of mesoscopic, two-dimensional electronic systems at high magnetic fields. Our samples, prepared from a low-mobility InGaAs/InAlAs wafer, exhibit reproducible, sample specific, resistance fluctuations. Focusing on the lowest Landau level we find that, while the diagonal resistivity displays strong fluctuations, the Hall resistivity is free of fluctuations and remains quantized at its $\nu=1$ value, $h/e^{2}$. This is true also in the insulating phase that terminates the quantum Hall series. These results extend the validity of the semicircle law of conductivity in the quantum Hall effect to the mesoscopic regime.