Intra-Landau level magnetoexcitons and the transition between quantum Hall states in undoped bilayer graphene

We study the collective modes of the quantum Hall states in undoped bilayer graphene in a strong perpendicular magnetic and electric field. Both for the well-known ferromagnetic state that is relevant for small electric field $E_\perp$ and the analogous valley/layer polarized one suitable for large $E_\perp$, the low energy physics is dominated by magnetoexcitons with zero angular momentum that are even combinations of excitons that conserve Landau orbitals. We identify a long wave length instability in both states, and argue that there is an intermediate range of the electric field $E^{(1)}_\text{c} < E_\perp < E^{(2)}_\text{c}$ where a gapless phase interpolates between the incompressible quantum Hall states. The experimental relevance of this crossover via a gapless state is discussed.