The quantum Hall effect under the influence of a top-gate and integrating AC lock-in measurements

TL;DR

This paper analyzes how a top-gate and AC lock-in measurement techniques influence the observed quantum Hall effect, revealing inflection points in Hall curves unrelated to Landau level density distributions.

Contribution

It introduces a theoretical calculation of the impact of a top-gate and AC lock-in measurements on the quantum Hall effect, highlighting features in Hall curves that are not directly tied to density of states.

Findings

Inflection points appear at the mean between integer plateaus in Hall curves.

The inflection points are not necessarily related to Landau level density distributions.

The study provides insights into measurement effects on quantum Hall observations.

Abstract

Low frequency AC-measurements are commonly used to determine the voltage and currents through mesoscopic devices. We calculate the effect of the alternating Hall voltage on the recorded time-averaged voltage in the presence of a top-gate covering a large part of the device. The gate is kept on a constant voltage, while the Hall voltage is recorded using an integrating alternating-current lock-in technique. The resulting Hall curves show inflection points at the arithmetic mean between two integer plateaus, which are not necessarily related to the distribution of the density of states within a Landau level.