| 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. In particular, at high magnetic fields, a perpendicular electric field (D) drives transitions between valley-unpolarized and valley-polarized states in several QH phases. I will describe a recent study where we explore the behavior of these transitions as the magnetic field B is reduced, focusing on the phases in the filling-factor range 1<ν<2. We find that as B is lowered, the variation of the critical electric field (D*) with filling factor exhibits a puzzling change of trend, from increasing to decreasing; near 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 B and D, and find that a valley-coherent phase may emerge for D ∼ D* in the high B regime. This suggests the existence of a Kekule bond-ordered phase, similarly to the phases recently observed in the ν=0 phase through STM measurements. |