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

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.