Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene

TL;DR

This paper proposes a new non-Abelian fractional quantum Hall state in multilayer graphene, explaining experimental observations and predicting phase transitions, offering a novel route to exotic particles without topological superconductivity.

Contribution

It introduces a parton fractional quantum Hall state in multilayer graphene as a new mechanism for non-Abelian particles, distinct from existing topological superconductor-based proposals.

Findings

The parton state explains the 1/2 FQH effect in bilayer graphene.

Prediction of non-Abelian FQH states in trilayer graphene.

Identification of experimental signatures and phase transitions.

Abstract

The current proposals for producing non-Abelian anyons and Majorana particles, which are neither fermions nor bosons, are primarily based on the realization of topological superconductivity in two dimensions. We show theoretically that the unique Landau level structure of bilayer graphene provides a new possible avenue for achieving such exotic particles. Specifically, we demonstrate the feasibility of a "parton" fractional quantum Hall (FQH) state, which supports non-Abelian particles without the usual topological superconductivity. Furthermore, we advance this state as the fundamental explanation of the puzzling $1/2$ FQH effect observed in bilayer graphene [Kim {\em et al.}, Nano Lett. {\bf 15}, 7445 (2015)], and predict that it will also occur in trilayer graphene. We indicate experimental signatures that differentiate the parton state from other candidate non-Abelian FQH states and predict that a transverse electric field can induce a topological quantum phase transition between two distinct non-Abelian FQH states.