Higher-Order States in the Multiple-Series, Fractional, Quantum Hall Effect

Abstract

We report results on the fractional quantum Hall effect in GaAs-${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ heterostructures at fractional Landau-level filling factor $\nu =\frac{p}{q}$ obtained with the combination of a dilution refrigerator and the National Magnet Laboratory hybrid magnet. We establish conclusively the quantiztation of the higher-order states $p$ in the series $q$. The Hall resistance is accurately quantized to 2.3 parts in ${10}^4$ for the $\frac{2}{5}$ state and 1.3 in ${10}^3$ for the $\frac{3}{5}$ state. New structures are observed near $\nu =\frac{3}{7}, \frac{4}{7}, \frac{4}{9}, \mathrm{and} \frac{5}{9}$.