Widely Tunable Quantum Phase Transition from Moore-Read to Composite Fermi Liquid in Bilayer Graphene

TL;DR

This paper proposes a method to experimentally realize and control a quantum phase transition between the Moore-Read fractional quantum Hall state and a composite Fermi liquid in bilayer graphene, using tunable parameters like electric bias and magnetic field.

Contribution

It introduces a detailed model for the transition in bilayer graphene, including Landau level mixing and predicts a new anisotropic gapless phase near level crossings.

Findings

Identifies parameter regimes for experimental access to the transition.

Numerical evidence for a new anisotropic gapless phase.

Demonstrates tunability of the transition via electric bias and magnetic field.

Abstract

We develop a proposal to realise a widely tunable and clean quantum phase transition in bilayer graphene between two paradigmatic fractionalized phases of matter: the Moore-Read fractional quantum Hall state and the composite Fermi liquid metal. This transition can be realized at total fillings $\nu=\pm 3+1/2$ and the critical point can be controllably accessed by tuning either the interlayer electric bias or the perpendicular magnetic field values over a wide range of parameters. We study the transition numerically within a model that contains all leading single particle corrections to the band-structure of bilayer graphene and includes the fluctuations between the $n=0$ and $n=1$ cyclotron orbitals of its zeroth Landau level to delineate the most favorable region of parameters to experimentally access this unconventional critical point. We also find evidence for a new anisotropic gapless phase stabilized near the level crossing of $n=0/1$ orbits.