Fractional Quantum Hall Effect at ν=2+6 /13: The Parton Paradigm for the Second Landau Level

The unexpected appearance of a fractional quantum Hall effect (FQHE) plateau at ν=2+6/13 [A. Kumar et al., Phys. Rev. Lett. 105, 246808 (2010)PRLTAO0031-900710.1103/PhysRevLett.105.246808] offers a clue into the physical mechanism of the FQHE in the second Landau level (SLL). Here we propose a "3̄2̄111" parton wave function, which is topologically distinct from the 6/13 state in the lowest Landau level. We demonstrate the 3̄2̄111 state to be a good candidate for the ν=2+6/13 FQHE, and make predictions for experimentally measurable properties that can reveal the nature of this state. Furthermore, we propose that the "n̄2̄111" family of parton states naturally describes many observed SLL FQHE plateaus.