Fractional quantum Hall effect at Landau level filling $\nu =4/11$

We report low-temperature electronic transport results on the fractional quantum Hall effect of composite fermions at Landau level filling $\nu =4/11$ in a very high mobility and low density sample. Measurements were carried out at temperatures down to $15\mathrm{mK}$, where an activated magnetoresistance $R_{xx}$ and a quantized Hall resistance $R_{xy}$, within $1\%$ of the expected value of $h/(4/11)e^2$, were observed. The temperature dependence of the $R_{xx}$ minimum at $4/11$ yields an activation energy gap of $\sim 7\mathrm{mK}$. Developing Hall plateaus were also observed at the neighboring states at $\nu =3/8\mathrm{and}5/13$.

Figure 1

$R_{xx}$ and $R_{xy}$ in the magnetic field range of 5–14 T at $T=26\mathrm{mK}$. Representative fractions are marked by arrows.

Figure 2

$R_{xx}$ and $B\times d{R}_{xy}/dB$ in the regime of $3/7>\nu >1/3$.

Figure 3

(a) T dependence of $R_{xx}$ between $2/5>\nu >1/3$. Three traces are shown at $T=15,22,\mathrm{and}30\mathrm{mK}$. (b) Arrhenius plot for the $R_{xx}$ minimum at $\nu =4/11$. The linear fit to the data points yields an energy gap of $\sim 7\mathrm{mK}$.

Figure 4

Top panel: $R_{xx}$ between $2/5>\nu >1/3$ at 4 selected tilt angles in a 40 nm width quantum well. The position of the $4/11$ state is marked by arrow. Bottom left panel shows the definition of the background resistance $R_{av}$. The bottom right two panels show the relative $R_{xx}$ value of the $4/11$ state $R_{\nu =4/11}/R_{av}$ versus the total $B$ field $\left(B_{\mathrm{total}}\right)$ for the $40\mathrm{and}50\mathrm{nm}$ QW samples, respectively.