Experimental studies of the fractional quantum Hall effect in the first excited Landau level

We present a spectrum of experimental data on the fractional quantum Hall effect (FQHE) states in the first excited Landau level, obtained in an ultrahigh mobility two-dimensional electron system and at very low temperatures, and report the following results. For the even-denominator FQHE states, the sample dependence of the $\ensuremath{\nu}=5∕2$ state clearly shows that disorder plays an important role in determining the energy gap at $\ensuremath{\nu}=5∕2$. For the developing $\ensuremath{\nu}=19∕8$ FQHE state, the temperature dependence of the ${R}_{xx}$ minimum implies an energy gap of $\ensuremath{\sim}5\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$. The energy gaps of the odd-denominator FQHE states at $\ensuremath{\nu}=7∕3$ and $8∕3$ also increase with decreasing disorder, similar to the gap at $5∕2$ state. Unexpectedly and contrary to earlier data on lower mobility samples, in this ultrahigh quality specimen, the $\ensuremath{\nu}=13∕5$ state is missing, while its particle-hole conjugate state, the $\ensuremath{\nu}=12∕5$ state, is a fully developed FQHE state. We speculate that this disappearance might indicate a spin polarization of the $\ensuremath{\nu}=13∕5$ state. Finally, the temperature dependence is studied for the two-reentrant integer quantum Hall states around $\ensuremath{\nu}=5∕2$ and is found to show a very narrow temperature range for the transition from quantized to classical value.