Fractional quantum Hall effect of partons and the nature of the 8/17 state in the zeroth Landau level of bilayer graphene

Abstract

We consider the fractional quantum Hall effect (FQHE) at the filling factor $8/17$, where signatures of incompressibility have been observed in the zeroth Landau level of bilayer graphene. We propose an Abelian state described by the ``$\overline{(8/3)}\bar{2}{1}^3$" parton wave function, where a parton itself forms an FQHE state. This state is topologically distinct from the $8/17$ Levin-Halperin state, a daughter state of the Moore-Read state. We carry out extensive numerical exact diagonalization of the Coulomb interaction at 8/17 in the zeroth Landau level of bilayer graphene but find that our results cannot conclusively determine the topological order of the underlying ground state. We work out the low-energy effective theory of the $\overline{(8/3)}\bar{2}{1}^3$ edge and make predictions for experimentally measurable properties of the state which can tell it apart from the 8/17 Levin-Halperin state.

arXiv comment9 pages, 2 figures and includes supplemental material

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• Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
• Unlocking new regimes in fractional quantum Hall effect with quaternions
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• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
• Dispersion of collective modes in spinful fractional quantum Hall states on the sphere
• Even-denominator fractional quantum Hall states in the zeroth Landau level of ABA trilayer graphene
• Time-dependent conserved operators for autonomous systems and quantization of resistance