Fractional quantum Hall effect in very-low-density GaAs/AlxGa1-xAs heterostructures

We report an experimental study of the quantum Hall effect in very-high-quality GaAs/AlxGa1-xAs heterostructures in an extremely-low-electron- density regime. At a temperature of 28 mK, the fractional quantum Hall states at Landau-level filling factors =2/3 and 1/3 are observed at a density as low as 7.0×109 cm-2, and the integral quantum Hall states at =2 and 1 are observed at a density as low as 4.0×109 cm-2. The possibilities of the even-denominator quantization in the lowest (<2) and second (2<<4) Landau levels in the very-low-density regime have also been investigated. Near the fractional filling factors =1/2, 3/2, 3/4, and 5/8, we observe weak inflection points in the Hall resistivity which lie on the classical Hall line, but we do not observe an activated temperature dependence for the diagonal resistivity. The previously reported even-denominator quantization at =5/2 is observed at a density as low as 1.3×1011 cm-2. We also report evidence for the development of new fractional quantum Hall states at =8/11 and 8/13. The =8/13 state belongs to a new (inner) branch of higher-order hierarchical states emanating from the =2/3 parent state.