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

We report ultralow temperature experiments on the obscure fractional quantum Hall effect at Landau level filling factor $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}5/2$ in a very high-mobility specimen of $\ensuremath{\mu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.7\ifmmode\times\else\texttimes\fi{}{10}^{7}{\mathrm{cm}}^{2}/\mathrm{V}\mathrm{s}$. We achieve an electron temperature as low as $\ensuremath{\sim}4\mathrm{mK}$, where we observe vanishing ${R}_{\mathrm{xx}}$ and, for the first time, a quantized Hall resistance, ${R}_{\mathrm{xy}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}h/(5/2){e}^{2}$ to within 2 ppm. ${R}_{\mathrm{xy}}$ at the neighboring odd-denominator states $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}7/3$ and $8/3$ is also quantized. The temperature dependences of the ${R}_{\mathrm{xx}}$ minima at these fractional fillings yield activation energy gaps ${\ensuremath{\Delta}}_{5/2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.11$, ${\ensuremath{\Delta}}_{7/3}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.10$, and ${\ensuremath{\Delta}}_{8/3}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.055\mathrm{K}$.