Direct comparison of fractional and integer quantized Hall resistance

We present precision measurements of the fractional quantized Hall effect, where the quantized resistance {{R}^{≤ft[ 1/3 \right]}} 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  ±  6.3) 10^-8 (95% confidence level) was obtained for the ratio ({{R}^{≤ft[ 1/3 \right]}}/6{{R}^[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 upcoming revision of the SI.