Quantum resistance standard accuracy close to the zero-dissipation state

Abstract

We report on a comparison of four GaAs/AlGaAs-based quantum resistance standards using an original technique adapted from the well-known Wheatstone bridge. This work shows that the quantized Hall resistance at Landau level filling factor ν=2 can be reproducible with a relative uncertainty of 32×10−12 in the dissipationless limit of the quantum Hall effect regime. In the presence of a very small dissipation characterized by a mean macroscopic longitudinal resistivity Rxx(B)¯ of a few μΩ, the discrepancy ΔRH(B) between quantum Hall resistors measured on the Hall plateau at magnetic induction B turns out to follow the so-called resistivity rule Rxx(B)¯=αB×d(ΔRH(B))/dB. While the dissipation increases with the measurement current value, the coefficient α stays constant in the range investigated (40−120 μA). This result enlightens the impact of the dissipation emergence in the two-dimensional electron gas on the Hall resistance quantization, which is of major interest for the resistance metrology. The quantum Hall effect is used to realize a universal resistance standard only linked to the electron charge e and the Planck constant h and it is known to play a central role in the upcoming revised Système International of units. There are therefore fundamental and practical benefits in testing the reproducibility property of the quantum Hall effect with better and better accuracy.