Exact Quantization of Even-Denominator Fractional Quantum Hall State at $\nu$=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 $\nu$=5/2 in a very high mobility specimen of $\mu =1.7\times 10^7$ 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 $\nu$=7/3 and 8/3 is also quantized. The temperature dependences of the $R_{xx}$-minima at these fractional fillings yield activation energy gaps ${\Delta }_{5/2}$=0.11K, ${\Delta }_{7/3}$=0.10K, and ${\Delta }_{8/3}$=0.055K.

5 pages, 3 figures