Quantum resistance standard accuracy close to the zero-dissipation state

TL;DR

This study demonstrates that quantum Hall resistance standards based on GaAs/AlGaAs can achieve near-zero dissipation accuracy with uncertainties as low as 32 parts in 10^12, confirming the robustness of the quantum Hall effect for resistance metrology.

Contribution

The paper introduces an original Wheatstone bridge technique to compare quantum resistance standards, revealing reproducibility at extremely low uncertainty levels close to the dissipationless state.

Findings

Reproducibility of quantum Hall resistance at 32×10^{-12} uncertainty.

Discrepancy follows resistivity rule with small dissipation.

Dissipation impact on quantization remains constant with current.

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 $\nu=2$ can be reproducible with a relative uncertainty of $32\times 10^{-12}$ 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 $\bar{R_{xx}(B)}$ of a few $\mu\Omega$, the discrepancy $\Delta R_{\mathrm{H}}(B)$ measured on the Hall plateau between quantum Hall resistors turns out to follow the so-called resistivity rule $\bar{R_{xx}(B)}=\alpha B\times d(\Delta R_{\mathrm{H}}(B))/dB$. While the dissipation increases with the measurement current value, the coefficient $\alpha$ stays constant in the range investigated ($40-120 \mathrm{\mu A}$). 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 \emph{e} and the Planck's constant \emph{h} and it is known to play a central role in the upcoming revised \emph{Syst\`eme 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.