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

Abstract

We report an experimental study of the quantum Hall effect in very-high-quality GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As heterostructures in an extremely-low-electron-density regime. At a temperature of \ensuremath{\sim}28 mK, the fractional quantum Hall states at Landau-level filling factors \ensuremath{\nu}=2/3 and 1/3 are observed at a density as low as 7.0\ifmmode\times\else\texttimes\fi{}${10}^{9}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$, and the integral quantum Hall states at \ensuremath{\nu}=2 and 1 are observed at a density as low as 4.0\ifmmode\times\else\texttimes\fi{}${10}^{9}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$. The possibilities of the even-denominator quantization in the lowest (\ensuremath{\nu}2) and second (24) Landau levels in the very-low-density regime have also been investigated. Near the fractional filling factors \ensuremath{\nu}=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 \ensuremath{\nu}=5/2 is observed at a density as low as 1.3\ifmmode\times\else\texttimes\fi{}${10}^{11}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$. We also report evidence for the development of new fractional quantum Hall states at \ensuremath{\nu}=8/11 and 8/13. The \ensuremath{\nu}=8/13 state belongs to a new (inner) branch of higher-order hierarchical states emanating from the \ensuremath{\nu}=2/3 parent state.