Fractional Quantum Hall Effect of Composite Fermions

In a $\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ quantum well of density $1\times {10}^{11}{\mathrm{c}\mathrm{m}}^{-2}$ we observed a fractional quantum Hall effect (FQHE) at $\nu =4/11$ and $5/13$, and weaker states at $\nu =6/17$, $4/13$, $5/17$, and $7/11$. These sequences of fractions do not fit into the standard series of integral quantum Hall effects of composite fermions (CF) at $\nu =p/(2mp\pm 1)$. They rather can be regarded as the FQHE of CFs attesting to residual interactions between these composite particles. In tilted magnetic fields the $\nu =4/11$ state remains unchanged, strongly suggesting it to be spin polarized. The weak $\nu =7/11$ state vanishes quickly with tilt.

Figure 1

$R_{xx}$ in the regime $2/3>\nu >2/7$ at $T\sim 35\mathrm{m}\mathrm{K}$. Major fractions are marked by arrows. Dashed traces are the Hall resistance $R_{xy}$ around $\nu =7/11$ and $\nu =4/11$.

Figure 2

(a) $T$ dependence of $R_{xx}$ around $\nu =4/11$. Three temperature traces are shown: solid line, 35 mK; dashed line, 70 mK; dotted line, 95 mK. (b) $T$ dependence of $R_{xx}$ around $\nu =7/11$. Four temperature traces are shown: solid line, 40 mK; dashed line, 70 mK; dotted line, 105 mK; dash-dotted line, 185 mK.

Figure 3

$R_{xx}$ between $2/5>\nu >1/3$ at five selected tilt angles. A total of 18 tilt angles were actually measured. Position of the $\nu =4/11$ state is marked by arrow.