Competing Laughlin state and Wigner crystal in Bernal bilayer graphene

Abstract

We study the fractional quantum Hall effect in the central Landau level of AB stacked (Bernal) bilayer graphene. By tuning the external applied magnetic field and the electric bias between the two layers one can access a regime where there is a degeneracy between Landau levels with orbital characters corresponding to $N=0$ and $N=1$ Galilean- Landau levels. While the Laughlin state is generically the ground state for filling $\ensuremath{\nu}=1/3$ we find that it can be destroyed and replaced by a Wigner crystal at the same filling factor by tuning the bias and applied field. This competition does not take place at $\ensuremath{\nu}=2/3$ where the incompressible ground state remains stable. The possibility of electrically inducing the Wigner crystal state opens a new range of studies of this state of matter.