Phase Diagram of the ν=2 quantum Hall phase in bilayer graphene

Bilayer graphene exhibits a rich phase diagram in the quantum Hall (QH) regime, arising from the interplay of the spin, valley, and orbital degrees of freedom. In particular, at very high magnetic fields, a perpendicular electric field drives a transition between valley-unpolarized and valley-polarized states in several QH phases. Here, we explore the behavior of this transition as the magnetic field $B$ is reduced, focusing on the phases around ν=2. We find that the variation of the critical electric field (D*) with filling factor is qualitatively different at lower B, and that for ν=2, D* may even vanish if B is sufficiently small. We present a theoretical model for the lattice-scale interactions which correctly accounts for these surprising observations; contrary to earlier studies, it involves finite-ranged terms comprising both repulsive and attractive components. Furthermore, we (theoretically) analyze the nature of the ν=2 state as a function of the magnetic and electric fields, and find that a valley-coherent phase may emerge in the D*~0 regime. This suggests the existence of a Kekule bond-ordered phase at low magnetic fields. Such phases have been recently observed in the ν=0 phase of monolayer graphene through STM measurements.