Influence of voltmeter impedance on quantum Hall measurements

We report the influence of voltmeters on measurements of the longitudinal resistance Rxx in the quantum Hall-effect regime. We show that for input resistances typical of standard digital lock-in amplifiers, Rxx can show a nonzero minimum which might be mistaken for a parallel conduction in the doping layer. This residual impedance at the Rxx minima can be calculated with Zres=Rxy2∕Rin+jωCRxy2, where Rin is the input resistance of the voltmeter, C is the measurement capacitance, and Rxy=h/νe2 is the Hall resistance. In contrast to a real parallel conduction, the effect disappears when either the current source and ground contact are swapped or the polarity of the magnetic field is changed; examples with data are shown. We discuss how proper phasing of a lock-in amplifier is necessary to eliminate false residual minima which arise from stray capacitances.