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.

arXiv comment7 pages, 2 figures

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• Composite-fermion pairing at half and quarter filled lowest Landau level
• Competition between fractional quantum Hall liquid and electron solid phases in the Landau levels of multilayer graphene
• Fractional quantum Hall effect of partons and the nature of the 8/17 state in the zeroth Landau level of bilayer graphene
• Unlocking new regimes in fractional quantum Hall effect with quaternions
• Static structure factor and the dispersion of the Girvin-MacDonald-Platzman density mode for fractional quantum Hall fluids on the Haldane sphere
• Numerical demonstration of Abelian fractional statistics of composite fermions in the spherical geometry
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
• Composite fermions and parton wavefunctions in twisted graphene on hexagonal boron nitride