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

We consider the fractional quantum Hall effect (FQHE) at the filling factor $8\mathrm{/}17$, where signatures of incompressibility have been observed in the zeroth Landau level of bilayer graphene. We propose an Abelian state described by the ``$\overline{(8\mathrm{/}3)}\bar{2}{1}^3$" parton wave function, where a parton itself forms an FQHE state. This state is topologically distinct from the $8\mathrm{/}17$ 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 $\overline{(8\mathrm{/}3)}\bar{2}{1}^3$ edge and make predictions for experimentally measurable properties of the state which can tell it apart from the 8/17 Levin-Halperin state.