We present activation gap measurements of the fractional quantum Hall effect (FQHE) in the second Landau level. Signatures for 14 (5) distinct incompressible FQHE states are seen in a high- (low-) mobility sample with the enigmatic $5∕2$ even-denominator FQHE having a large activation gap of $\sim 500$ $(\sim 250)\mathrm{mK}$ in the high- (low-) mobility sample. This is the largest gap ever reported for the $5∕2$ FQHE state. Our measured large relative gaps for $5∕2$, $7∕3$, and $8∕3$ FQHEs indicate the emergence of exotic FQHE correlations in the second Landau level, possibly different from the well-known lowest-Landau-level Laughlin correlations. Our measured $5∕2$ gap is found to be in reasonable agreement with the theoretical gap once finite-width and disorder-broadening corrections are taken into account.

• Received 2 July 2007

DOI:https://doi.org/10.1103/PhysRevB.77.081301