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

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 state to a non-Abelian parton state can be induced at filling factors ν=1/2,  2/5 and 3/7. The parton states host exotic anyons that could potentially form building blocks of a fault-tolerant topological quantum computer. Intriguingly, some of these transitions may have been observed in a recent experiment [Huang et al. arXiv:2105.07058].