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

Abstract

We report results on the fractional quantum Hall effect in GaAs-${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ heterostructures at fractional Landau-level filling factor $\ensuremath{\nu}=\frac{p}{q}$ 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 $\ensuremath{\nu}=\frac{3}{7}, \frac{4}{7}, \frac{4}{9}, \mathrm{and} \frac{5}{9}$.