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

TL;DR

This paper explores the fractional quantum Hall effect at filling factor 8/17 in bilayer graphene, proposing a novel parton wave function and analyzing its properties, but faces challenges in conclusively identifying the topological order.

Contribution

It introduces a new Abelian parton wave function for the 8/17 state and analyzes its theoretical and experimental signatures in bilayer graphene.

Findings

Numerical results are inconclusive about the topological order.

The proposed edge theory predicts measurable differences from other states.

The study advances understanding of the 8/17 fractional quantum Hall state.

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.