A non-Abelian fractional quantum Hall state at $3/7$ filled Landau level

TL;DR

This paper proposes a new non-Abelian fractional quantum Hall state at filling factor 3/7 in the second Landau level, which outperforms standard models and could explain future experimental observations.

Contribution

The authors introduce a novel non-Abelian candidate state at 3/7 filling, showing its energetic favorability and good match with numerical ground states in the second Landau level.

Findings

The proposed state is energetically superior to the Jain composite-fermion state.

It closely matches the ground state in exact diagonalization studies.

Predicted measurable properties can verify the state's topological structure.

Abstract

We consider a non-Abelian candidate state at filling factor $\nu=3/7$ state belonging to the parton family. We find that, in the second Landau level of GaAs (i.e. at filling factor $\nu=2+3/7$), this state is energetically superior to the standard Jain composite-fermion state and also provides a very good representation of the ground state found in exact diagonalization studies of finite systems. This leads us to predict that \emph{if} a fractional quantum Hall effect is observed at $\nu=3/7$ in the second Landau level, it is likely to be described by this new non-Abelian state. We enumerate experimentally measurable properties that can verify the topological structure of this state.