The Gap at nu = 5/2 and the Role of Disorder in Fractional Quantum Hall States

Theoretical results for the gaps of fractional quantum Hall states are substantially larger than experimental values determined from the activated behaviour of charge transport. The disparity in the case of the enigmatic nu = 5/2 state is worrying as it amounts to a factor 20 to 30. We argue that disorder effects are responsible for this disparity and show how intrinsic gaps can be extracted from the measured transport gaps of particle-hole symmetric states within the same Landau level. We present new theoretical results for gaps at nu = 5/2 and 7/2, as well as at nu = 1/3, 2/5, 3/7 and 4/9, based on exact diagonalizations, taking account of the finite thickness of the two-dimensional electron layer and Landau level mixing effects. We find these to be consistent with the intrinsic gaps inferred from measured transport gaps. While earlier analyses (Du et al, Phys. Rev. Lett. 70, 2944 (1993)) assumed constant broadening for each sample, our results for the disorder broadening depend on the filling fraction, and appear to scale with the charge of the elementary excitations of the corresponding fractional state. This result is consistent with quasiparticle mediated dissipative transport.