Disorder and the fractional quantum Hall effect: Activation energies and the collapse of the gap

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Abstract
We examine the broadening of the collective excitations of a fractional quantum Hall state due to disorder. Because of the absence of screening at long wavelength in this regime, we believe that the broadening depends mostly on the ionized impurity contribution to the disorder potential. The broadening of the collective excitation spectrum reduces the minimum excitation energy and eventually the gap required for the occurrence of the fractional quantum Hall effect collapses. We present some results on the necessary conditions for the gap to remain finite. These depend on some exact sum rules for three-point correlation functions of isotropic states constructed entirely within the lowest Landau level. Finally the relationship between our results and the activation energies seen in the magnetotransport coefficients is discussed.