Exact Quantization of the Even-Denominator Fractional Quantum Hall State at $\mathit{\nu }=5\mathrm{}/2$ Landau Level Filling Factor

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