Broken symmetry states in bilayer graphene in electric and in-plane magnetic fields

Broken symmetry states in bilayer graphene in perpendicular electric E-perpendicular to and in-plane magnetic B-parallel to fields are studied in the presence of the dynamically screened long-range Coulomb interaction and the symmetry-breaking contact four-fermion interactions. The integral gap equations are solved numerically, and it is shown that the momentum dependence of gaps is essential: It diminishes by an order of magnitude the gaps compared to the case of momentum-independent approximation, and the obtained gap magnitudes are found to agree well with existing experimental values. We derived a phase diagram of bilayer graphene at the neutrality point in the plane (B-parallel to, E-perpendicular to) showing that the (canted) layer antiferromagnetic (LAF) state remains a stable ground state of the system at large B-parallel to. On the other hand, while the LAF phase is realized at small values of E-perpendicular to, the quantum valley Hall (QVH) phase is the ground state of the system at values E-perpendicular to > E-cr (B-parallel to), where a critical value E-cr (B-parallel to) increases with in-plane magnetic field B-parallel to.