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 [Kumar et al., Phys. Rev. Lett. 105, 246808 (2010)] offers a clue into the physical mechanism of the FQHE in the second Landau level (SLL). Here we propose a ``bar3bar2111'' parton wave function and demonstrate it to be a good candidate state for this phase. We make several predictions for experimentally measurable properties that can reveal the nature of this state and also distinguish it from the topologically distinct 6/13 state realized in the lowest Landau level. Taking these results together with the recent demonstration that the related ``bar2bar2111'' wave function is a good candidate for the ground state at ν=2+1/2 [Balram et al., Phys. Rev. B 98, 035127 (2018)], we propose that the ``bar{n}bar2111'' family of parton wave functions naturally describes the experimentally observed sequence of SLL FQHE plateaus at 2+2/3, 2+1/2 and 2+6/13, and their hole partners.