Parton wave function for the fractional quantum Hall effect at $\nu=6/17$

Abstract

We consider the fractional quantum Hall effect at the filling $\nu=6/17$, where experiments have observed features of incompressibility in the form of a minimum in the longitudinal resistance. We propose a parton state denoted as "$3\bar{2}1^{3}$" and show it to be a feasible candidate to capture the ground state at $\nu=6/17$. We work out the low-energy effective theory of the $3\bar{2}1^{3}$ edge and make several predictions for experimentally measurable properties of the state which can help detect its underlying topological order. Intriguingly, we find that the $3\bar{2}1^{3}$ state likely lies in the same universality class as the state obtained from composite-fermionizing the 1+1/5 Laughlin state.