Prediction of non-Abelian fractional quantum Hall effect at $\nu = 2 + \frac{4}{11}$

TL;DR

This paper investigates a theoretical non-Abelian fractional quantum Hall state at filling factor 4/11 in the second Landau level, proposing it as a viable candidate and predicting measurable properties to distinguish it from other states.

Contribution

It introduces and analyzes a new non-Abelian parton state at 4/11 in the SLL, not previously studied, and predicts experimental signatures to identify it.

Findings

The 4/11 non-Abelian state could be energetically competitive with other candidates.

Predicted measurable properties can distinguish this state from other topological orders.

The state remains a viable candidate despite lack of experimental observation so far.

Abstract

The fractional quantum Hall effect (FQHE) in the second Landau level (SLL) likely stabilizes non-Abelian topological orders. Recently, a parton sequence has been proposed to capture many of the fractions observed in the SLL [Ajit C. Balram, SciPost Phys. {\bf 10}, 083 (2021)]. We consider the first member of this sequence which has not yet been studied, which is a non-Abelian state that occurs at $4/11$. As yet FQHE in the SLL at this fraction has not been observed in experiments. Nevertheless, by studying its competition with other candidate FQHE states in the SLL we show that this parton state might be viable. We also make predictions for experimentally measurable properties of the parton state which can distinguish it from other topological orders.