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

TL;DR

This study demonstrates the precise quantization of the fractional quantum Hall effect at filling factor 5/2 at ultra-low temperatures, confirming the existence of an even-denominator state with quantized Hall resistance.

Contribution

First experimental observation of exact quantization of the 5/2 fractional quantum Hall state at ultra-low temperatures in a high mobility sample.

Findings

Quantized Hall resistance at $ u$=5/2 within 2 ppm

Activation energy gap for $ u$=5/2 is 0.11K

Quantization observed at neighboring odd-denominator states

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.