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

We report results on the fractional quantum Hall effect in GaAs-AlₓGa_1-xAs heterostructures at fractional Landau-level filling factor ν=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 10⁴ for the 2/5 state and 1.3 in 10³ for the 3/5 state. New structures are observed near ν=3/7, 4/7, 4/9, and 5/9.