Quantum Hall ferroelectric helix in bilayer graphene

We reexamine the nature of the ground states of bilayer graphene at odd integer filling factors within a simplified model of nearly degenerate n = 0 and n = 1 Landau levels. Previous Hartree-Fock studies have found that ferroelectric states with orbital coherence can be stabilized by tuning the orbital splitting between these levels. These studies indicated that, in addition to a uniform ferroelectric state, a helical ferroelectric phase with spontaneously broken translational symmetry is possible. By performing exact diagonalization on the torus, we argue that the system does not have a uniform coherent state but instead transitions directly from the uniform incoherent state into the ferroelectric helical phase. We argue that there is a realistic prospect to stabilize the helical ferroelectric state in bilayer graphene by tuning the interlayer electric field in a model that includes all single-particle corrections to its zero energy eightfold multiplet of Landau levels.