A non-Abelian parton state for the $\nu=2+3/8$ fractional quantum Hall effect

TL;DR

This paper proposes a non-Abelian parton wave function as a candidate ground state for the fractional quantum Hall effect at filling factor 2+3/8, supported by numerical evidence and predictions for experimental verification.

Contribution

It introduces a novel non-Abelian parton state for the 2+3/8 FQHE and demonstrates its feasibility as the ground state through numerical analysis.

Findings

Numerical evidence supports the $ar{3}ar{2}^{2}1^{4}$ state as a candidate ground state.

Predictions made for experimental signatures of the topological order.

The state explains the observed quantized Hall plateau at $ u=2+3/8$.

Abstract

Fascinating structures have arisen from the study of the fractional quantum Hall effect (FQHE) at the even denominator fraction of $5/2$. We consider the FQHE at another even denominator fraction, namely $\nu=2+3/8$, where a well-developed and quantized Hall plateau has been observed in experiments. We examine the non-Abelian state described by the "$\bar{3}\bar{2}^{2}1^{4}$" parton wave function and numerically demonstrate it to be a feasible candidate for the ground state at $\nu=2+3/8$. We make predictions for experimentally measurable properties of the $\bar{3}\bar{2}^{2}1^{4}$ state that can reveal its underlying topological structure.