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

TL;DR

This paper introduces a novel parton wave function model to explain the fractional quantum Hall effect at a7=2+6/13 in the second Landau level, providing insights into its topological nature and predicting measurable properties.

Contribution

The paper proposes a new a7=2+6/13 state using the a7bar{3}a7bar{2}111 wave function, extending the parton paradigm to the second Landau level.

Findings

The a7bar{3}a7bar{2}111 state fits experimental data for a7=2+6/13.

Predictions for measurable properties distinguish the proposed state from other models.

The a7bar{n}a7bar{2}111 family describes multiple observed SLL FQHE plateaus.

Abstract

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