$nu=5\mathrm{/}2$ Fractional Quantum Hall State in Low-Mobility Electron Systems: Different Roles of Disorder

We report the observation of a fully developed fractional quantum Hall state at $\nu =5\mathrm{/}2$ in GaAs/Al${}_x$Ga${}_{1-x}$As quantum wells with mobility well below ${10}^7$\thinspace cm${}^2$/Vs. This is achieved either by strong illumination or reducing the barrier Al composition without illumination. We explain both results in terms of screening of the ionized remote impurity (RI) potential by nearby neutral shallow donors. Despite the dramatic improvement in the transport features, the energy gap ${\mathrm{\Delta }}_{5\mathrm{/}2}$ is limited to a rather small value ($\sim 100$ mK), which indicates that once the RI potential is well screened and the $5\mathrm{/}2$ state emerges, the size of ${\mathrm{\Delta }}_{5\mathrm{/}2}$ is limited by the mobility, i.e., by background impurities.