Direct Comparison of Fractional and Integer Quantized Hall Resistance

TL;DR

This study performs a highly precise comparison between fractional and integer quantum Hall resistances, providing critical insights into fundamental physics and the SI redefinition, using advanced cryogenic measurement techniques.

Contribution

It presents the most precise direct comparison of fractional and integer quantum Hall resistances, validating fundamental physics with a novel cryogenic current comparator bridge.

Findings

Achieved a ratio measurement with a 95% confidence level uncertainty of 6.3×10^{-8}.

Demonstrated the capability of cryogenic current comparator bridges for ultra-precise resistance comparisons.

Confirmed the consistency of fractional and integer quantum Hall effects within experimental uncertainty.

Abstract

We present precision measurements of the fractional quantized Hall effect where the quantized resistance $R^{[1/3]}$ in the fractional quantum Hall state at filling factor 1/3 was compared with a quantized resistance $R^{[2]}$, represented by an integer quantum Hall state at filling factor 2. A cryogenic current comparator bridge capable of currents down to the nanoampere range was used to directly compare two resistance values of two GaAs-based devices located in two cryostats. A value of $1 - (5.3 \pm 6.3) 10^{-8}$ (95% confidence level) was obtained for the ratio $(R^{[1/3]}/6R^{[2]})$. This constitutes the most precise comparison of integer resistance quantization (in terms of $h/e^2$) in single-particle systems and of fractional quantization in fractionally charged quasi-particle systems. While not relevant for practical metrology, such a test of the validity of the underlying physics is of significance in the context of the up-coming revision of the SI.