Observation of incompressibility at $\nu =4/11$ and $\nu =5/13$

The region of filling factors $1/3<\nu <2/5$ is predicted to support new types of fractional quantum Hall states with topological order different from that of the Laughlin-Jain or the Moore-Read states. Incompressibility is a necessary condition for the formation of such novel topological states. We find that at 6.9 mK incompressibility develops only at $\nu =4/11$ and $5/13$, while the states at $\nu =6/17$ and $3/8$ remain compressible. Our observations at $\nu =4/11$ and $5/13$ are first steps towards understanding emergent topological order in these fractional quantum Hall states.

Figure 1

Longitudinal $\left(R_{xx}\right)$ and Hall $\left(R_{xy}\right)$ resistance in the filling factor range $1/3<\nu <1/2$ at 6.9 mK. Horizontal lines indicate the expected plateau-like behavior of the Hall resistance at $\nu =4/11$ and $\nu =5/13$.

Figure 2

Waterfall plot of $R_{xx}$ and $R_{xy}$ curves at several different temperatures in the $1/3<\nu <2/5$ range. The dashed lines mark $\nu =5/13,3/8,4/11$, and $6/17$ filling factors. Scales refer to the lowest-temperature data sets. For clarity, $R_{xx}$ traces are shifted vertically by $1\mathrm{k}\Omega$, while $R_{xy}$ traces are shifted by $2\mathrm{k}\Omega$ each relative to the trace of lower temperature.

Figure 3

Dependence of magnetoresistance on temperature at the filling factors $\nu =4/11,3/8$, and $5/13$. Lines are guides to the eye.

Figure 4

Arrhenius plot for $R_{xx}$ at $\nu =4/11$ and $\nu =5/13$ filling factors. Straight lines are used as guides for the eye representing the activated regions. The inset shows the scaling of the experimentally extracted gaps $\Delta$ at $\nu =4/11$ and $5/13$ states with the Coulomb energy $E_C$.