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

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.

7 pages, 2 figures

References in corpus (14)

• Non-Abelian Anyons and Topological Quantum Computation
• Experimental studies of the fractional quantum Hall effect in the first excited Landau level
• Fractional Quantum Hall Hierarchy and the Second Landau Level
• Fractional Quantum Hall Effect in the Second Landau Level
• Spinful Composite Fermions in a Negative Effective Field
• Fractional Quantum Hall Effect at Landau Level Filling nu=4/11
• Prediction of a non-Abelian fractional quantum Hall state with $f$-wave pairing of composite fermions in wide quantum wells
• Phase Diagram of Fractional Quantum Hall Effect of Composite Fermions in Multi-Component Systems
• Observation of Incompressibility at $\nu =4/11$ and $\nu =5/13$
• Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond
• A non-Abelian fractional quantum Hall state at $3/7$ filled Landau level
• Unconventional ${\mathbb{Z}}_n$ parton states at $\nu =7/3$: The role of finite width
• Increasing the ν = 5 / 2 gap energy: an analysis of MBE growth parameters
• Abelian parton state for the $\nu =4/11$ fractional quantum Hall effect

Cited by in corpus (1)

• Composite fermions and parton wavefunctions in twisted graphene on hexagonal boron nitride