Exact Quantization of Even-Denominator Fractional Quantum Hall State at $ν$=5/2 Landau Level Filling Factor

Abstract

We report ultra-low temperature experiments on the obscure fractional quantum Hall effect (FQHE) at Landau level filling factor $ν$=5/2 in a very high mobility specimen of $μ=1.7 \times 10^7$ cm$^2$/Vs. We achieve an electron temperature as low as $\sim$ 4~mK, where we observe vanishing $R_{xx}$ and, for the first time, a quantized Hall resistance, $R_{xy}=h/(5/2e^2)$ to within 2 ppm. $R_{xy}$ at the neighboring odd-denominator states $ν$=7/3 and 8/3 is also quantized. The temperature dependences of the $R_{xx}$-minima at these fractional fillings yield activation energy gaps $Δ_{5/2}$=0.11K, $Δ_{7/3}$=0.10K, and $Δ_{8/3}$=0.055K.

5 pages, 3 figures