Transitions from Abelian composite fermion to non-Abelian parton fractional quantum Hall states in the zeroth Landau level of bilayer graphene

TL;DR

This paper predicts a magnetic field-induced topological phase transition in bilayer graphene's zeroth Landau level, switching from Abelian to non-Abelian fractional quantum Hall states, with potential implications for quantum computing.

Contribution

It demonstrates the possibility of tuning between Abelian and non-Abelian quantum Hall states in bilayer graphene via magnetic field adjustments.

Findings

Topological quantum phase transition observed at specific filling factors.

Identification of non-Abelian parton states hosting exotic anyons.

Some transitions may have been experimentally observed already.

Abstract

The electron-electron interaction in the Landau levels of bilayer graphene is markedly different from that of conventional semiconductors such as GaAs. We show that in the zeroth Landau level of bilayer graphene, in the orbital which is dominated by the non-relativistic second Landau level wave function, by tuning the magnetic field a topological quantum phase transition from an Abelian composite fermion to a non-Abelian parton fractional quantum Hall state can be induced at filling factors $1/2, ~2/5$ and $3/7$. The parton states host exotic anyons that can potentially be utilized to store and process quantum information. Intriguingly, some of these transitions may have been observed in a recent experiment [Huang \emph{et al.} arXiv:2105.07058].