Nonconventional Odd-Denominator Fractional Quantum Hall States in the Second Landau Level

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.