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

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.

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• Hetero-Orbital Two-Component Fractional Quantum Hall States in Bilayer Graphene
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
• Numerical demonstration of Abelian fractional statistics of composite fermions in the spherical geometry
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