Effects of metallic gates on AC measurements of the quantum Hall resistance

Using a sample with a split back gate, a linear frequency dependence of the AC quantum Hall resistance (QHR) was observed. The frequency coefficient, which is due to dielectric losses produced by leakage current between the two-dimensional electron gas (2DEG) and the back gates, can be turned from a positive to a negative value by increasing the back-gate voltage. More interestingly, by removing these back gates, the losses can be considerably reduced, leading to a residual frequency coefficient on the order of (0.03±0.03)×10^-6/kHz. Moreover, at 1 kHz, an extremely flat plateau was observed over a magnetic field range of 1.4 T. These results clearly indicate that the audio frequency dependence of the QHR is to a large extent related to the measurement apparatus and does not originate from the physical transport properties of the 2DEG.