High-precision measurements of the quantized Hall resistance:Experimental conditions for universality

Abstract

We report comprehensive high-precision direct and indirect comparisons of quantized Hall resistances in Si-metal-oxide-semiconductor field-effect transistor and GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As heterostructures. We find no evidence for a step, device, or material dependence of the quantized Hall resistance (QHR) at the level of 3.5 parts in ${10}^{10}$ provided the resistance of each contact used is sufficiently low. However, we observe deviations from ideal QHR values of up to 5 parts in ${10}^{7}$ if the resistance of at least one of the voltage probes used in the measurement is in the k\ensuremath{\Omega} range. The deviations in the QHR are always accompanied by nonzero values for longitudinal voltage on at least one side of the sample. We propose that deviations such as these are responsible for reports in the literature that purport to show deviant QHR values with zero dissipation. The magnitude of the QHR deviations varies inversely with both current and temperature, for temperatures below 1.2 K and currents below the device critical current.