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

Broken symmetry states in bilayer graphene in perpendicular electric $E_\perp$ and in-plane magnetic $B_\parallel$ 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 $(B_\parallel,E_\perp)$ showing that the (canted) layer antiferromagnetic (LAF) state remains a stable ground state of the system at large $B_\parallel$. On the other hand, while the LAF phase is realized at small values of $E_{\perp}$, the quantum valley Hall (QVH) phase is the ground state of the system at values $E_{\perp}>E_{cr}(B_\parallel)$, where a critical value $E_{cr}(B_\parallel)$ increases with in-plane magnetic field $B_{||}$.