Nature of the anomalous $4/13$ fractional quantum Hall effect in graphene

TL;DR

This paper investigates the anomalous 4/13 fractional quantum Hall effect in graphene, proposing a partonic wave function model and predicting measurable edge properties to better understand this unconventional quantum state.

Contribution

It introduces a novel partonic wave function for the 4/13 FQHE in graphene and provides theoretical predictions for its experimental signatures.

Findings

Proposed a viable partonic wave function for 4/13 FQHE in graphene

Predicted edge state properties for experimental verification

Supported the model with Coulomb ground state analysis

Abstract

Extensive fractional quantum Hall effect (FQHE) has been observed in graphene-based materials. Some of the observed fractions are anomalous in that FQHE has not been established at these fractions in conventional GaAs systems. One such fraction is $4/13$, where incompressibility has recently been reported in graphene [Kumar et al., Nat. Comm. 9, 2776 (2018)]. We propose a partonic wave function at $4/13$ and show it to be a viable candidate to describe the Coulomb ground state. Using the effective edge theory, we make predictions for experimentally measurable properties of the state.