Doping lattice Read-Rezayi states with their minimal non-abelian anyons gives charge-2 or charge-k superconductors for even k, and for odd k either superconductivity or a charge-k Fermi liquid with period-(k+2) charge order, depending on which fusion channel wins.
Nonconventional odd denominator fractional quantum Hall states in the second Landau level
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We report the observation of a new fractional quantum Hall state in the second Landau level of a two-dimensional electron gas at the Landau level filling factor $\nu=2+6/13$. We find that the model of noninteracting composite fermions can explain the magnitude of gaps of the prominent 2+1/3 and 2+2/3 states. The same model fails, however, to account for the gaps of the 2+2/5 and the newly observed 2+6/13 states suggesting that these two states are of exotic origin.omposite fermion model. However, the weaker 2+2/5 and 2+6/13 states deviate significantly suggesting that these states are of exotic origin.
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Doping lattice non-abelian quantum Hall states
Doping lattice Read-Rezayi states with their minimal non-abelian anyons gives charge-2 or charge-k superconductors for even k, and for odd k either superconductivity or a charge-k Fermi liquid with period-(k+2) charge order, depending on which fusion channel wins.