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arXiv · 2404.15547

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

Ajit C. Balram·Nicolas Regnault
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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.

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Ajit C. Balram, Nicolas Regnault. 2024-04-23. Fractional quantum Hall effect of partons and the nature of the 8/17 state in the zeroth Landau level of bilayer graphene. https://doi.org/10.1103/physrevb.110.l081114

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