Precision comparison of the quantum Hall effect in graphene and gallium arsenide

TL;DR

This study compares the quantum Hall effect in graphene and gallium arsenide with high precision, confirming their resistance quantization is indistinguishable within extremely tight measurement uncertainty, supporting graphene's use in resistance standards.

Contribution

It provides the most precise comparison to date of quantum Hall resistance in graphene and GaAs, setting new limits on correction terms and validating graphene's metrological suitability.

Findings

No detectable difference in quantized resistance within $8.7\times 10^{-11}$

Graphene's quantum Hall effect matches GaAs with unprecedented precision

Supports use of graphene as a high-quality resistance standard

Abstract

The half-integer quantum Hall effect in epitaxial graphene is compared with high precision to the well known integer effect in a GaAs/AlGaAs heterostructure. We find no difference between the quantised resistance values within the relative standard uncertainty of our measurement of $8.7\times 10^{-11}$. The result places new tighter limits on any possible correction terms to the simple relation $R_{\rm K}=h/e^2$, and also demonstrates that epitaxial graphene samples are suitable for application as electrical resistance standards of the highest metrological quality. We discuss the characterisation of the graphene sample used in this experiment and present the details of the cryogenic current comparator bridge and associated uncertainty budget.