Widely Tunable Quantum Phase Transition from Moore-Read to Composite Fermi Liquid in Bilayer Graphene
Here, we develop a proposal to realize 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 $\textit{ν}$ = ±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 $\textit{n}$ = 0 and $\textit{n}$ = 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 $\textit{n}$ = 0/1 orbits.