Abstract
Bilayer graphene exhibits a rich phase diagram in the quantum Hall regime, arising from a multitude of internal degrees of freedom, including spin, valley, and orbital indices. The variety of fractional quantum Hall states between filling factors 1 < ν ≤ 2 suggests, among other things, a quantum phase transition between valley-unpolarized and polarized states at a perpendicular electric field D^*. We find the behavior of D^* with ν changes markedly as B is reduced. At ν = 2, D^* may even vanish when B is sufficiently small. We present a theoretical model for lattice-scale interactions which explains these observations; surprisingly, both repulsive and attractive components in the interactions are required. Within this model we analyze the nature of the ν = 2 state as a function of the magnetic and electric fields, and predict that valley-coherence may emerge for D ∼ D^* in the high B regime. This suggests the system supports Kekule bond-ordering, which could in principle be verified via STM measurements.