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 $\nu =2$ 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 $\overline{R_{xx}(B)}$ 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 $\overline{R_{xx}(B)}=\alpha B\times d(\Delta R_{\mathrm{H}}(B))/dB$. While the dissipation increases with the measurement current value, the coefficient $\alpha$ stays constant in the range investigated ($40-120\mu \mathrm{A}$). 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{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.

6 pages, 6 figures

Cited by in corpus (14)

• Quantum Hall resistance standards from graphene grown by chemical vapor deposition on silicon carbide
• Operation of graphene quantum Hall resistance standard in a cryogen-free table-top system
• Practical quantum realization of the ampere from the electron charge
• Exceptionally accurate large graphene quantum Hall arrays for the new SI
• The ampere and the electrical units in the quantum era
• Zero external magnetic field quantum standard of resistance at the 10-9 level
• A programmable quantum current standard from the Josephson and the quantum Hall effects
• Conductance oscillations in quantum point contacts of InAs/GaSb heterostructures
• A unified realization of electrical quantities from the quantum International System of Units
• Quantitative measurement of the thermal contact resistance between a glass microsphere and a plate
• Cavity Quantum Hall Hydrodynamics
• Improving Wheatstone Bridge Sensitivity with Computational Simulations and Bayesian Optimization
• HgTe quantum wells for QHE metrology under soft cryomagnetic conditions: permanent magnets and liquid ${}^{4}He$ temperatures
• Epitaxial graphene homogeneity and quantum Hall effect in millimeter-scale devices