Graphene surpasses GaAs/AlGaAs for the application of the quantum Hall effect in metrology

TL;DR

This paper demonstrates that high-quality graphene devices can outperform traditional GaAs/AlGaAs in quantum Hall effect applications, offering more practical, versatile, and accurate resistance standards for metrology based on fundamental constants.

Contribution

It shows that graphene can surpass GaAs/AlGaAs in operational conditions for quantum Hall resistance standards, supporting the universality of the effect and its use in SI redefinition.

Findings

Graphene devices achieve accurate quantization within 1e-9 over wide magnetic field ranges.

Operational conditions are significantly relaxed in graphene, with lower magnetic fields and higher temperatures.

The quantized Hall resistance in graphene agrees with GaAs/AlGaAs within 8.2e-11 uncertainty.

Abstract

The quantum Hall effect (QHE) theoretically provides a universal standard of electrical resistance in terms of the Planck constant $h$ and the electron charge $e$. In graphene, the spacing between the lowest discrete energy levels occupied by the charge carriers under magnetic field is exceptionally large. This is promising for a quantum Hall resistance standard more practical in graphene than in the GaAs/AlGaAs devices currently used in national metrology institutes. Here, we demonstrate that large QHE devices, made of high quality graphene grown by propane/hydrogen chemical vapour deposition on SiC substrates, can surpass state-of-the-art GaAs/AlGaAs devices by considerable margins in their required operational conditions. In particular, in the device presented here, the Hall resistance is accurately quantized within $1\times 10^{-9}$ over a 10-T wide range of magnetic field with a remarkable lower bound at 3.5 T, temperatures as high as 10 K, or measurement currents as high as 0.5 mA. These significantly enlarged and relaxed operational conditions, with a very convenient compromise of 5 T, 5.1 K and 50 $\mu$A, set the superiority of graphene for this application and for the new generation of versatile and user-friendly quantum standards, compatible with a broader industrial use. We also measured an agreement of the quantized Hall resistance in graphene and GaAs/AlGaAs with an ultimate relative uncertainty of $8.2\times 10^{-11}$. This supports the universality of the QHE and its theoretical relation to $h$ and $e$, essential for the application in metrology, particularly in view of the forthcoming Syst\`eme International d'unit\'es (SI) based on fundamental constants of physics, including the redefinition of the kilogram in terms of $h$.