Direct Comparison of Fractional and Integer Quantized Hall Resistance

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.