Universality of critical exponents in the fractional quantum Hall regime

Scaling for transitions between integer quantum Hall states (IQHSs) has been studied extensively, and measurements show that the universality of the critical exponents depends on the nature of the disorder present in the samples [1-3]. The situation is much more complex when we introduce electron-electron interaction, as is the case of the fractional quantum Hall states (FQHSs). Recent theoretical calculations suggest that the critical exponents obtained for the transitions between FQHSs are identical to those of the IQHSs, provided that the FQHSs can be viewed as the IQHSs of non-interacting composite fermions [4]. However, the latest experiments on high-quality 2DESs confined to GaAs quantum wells reveal that the exponents agree with the theoretical expected value only for a limited number of FQHS transitions [5].  Possible causes for the non-universality are the strongly interacting nature of the composite fermions, and the nature of the disorder [5]. In our work, we investigate this underlying non-universality for the transitions between the FQHSs by intentionally introducing short-range impurities in the quantum well where the electrons reside. We do so by systematically changing the Al concentration (x) in a series of Al_xGa_1-xAs quantum wells with 0  x  0.016. We find that the exponents vary with the alloy fraction, suggesting the interplay of disorder and interaction in the fractional quantum Hall regime.

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