Observation of filling factor 6/13 is one of the surprising fractional quantum Hall states in the second Landau level because, in contrast to the standard wisdom, the fractions $(\nu <1/2)$ with lower numerators, namely 4 and 5, have not yet been observed. We find that a state indeed forms at $\nu =6/13$ as an intermittent topological state between two prominent states at $\nu =1/2$ and $\nu =2/5$ with lower numerators. Also, we predict that a state forms at $\nu =5/13$ as an intermittent to $\nu =2/5$ and $\nu =3/8$. Our proposed wave functions for $\nu =6/13$ and $5/13$ have excellent overlaps with the corresponding exact ground state wave functions. The Chern-Simons coupling matrices deduced from the form of these wave functions are analyzed to predict the topological properties, which may be experimentally verified.

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• Edge states
• Fractional quantum Hall effect
• Landau levels
• Two-dimensional electron gas