Isospin and momentum polarized orders in bilayer graphene

Electron bands in the untwisted bilayer graphene flatten out in a transverse electric field, offering a promising platform for correlated electron physics. We predict that the spin/valley isospin magnetism, resembling that seen in moir\'{e} bands, coexists with momentum-polarized phases occurring via a ``flocking transition'' in momentum space. This transition results in the electron momentum distribution being spontaneously displaced relative to the $K$ and $K'$ valley centers. These phases feature unusual observables such as persistent currents in the ground state. Momentum-polarized carriers ``sample'' the Berry curvature of the conduction band, resulting in a unique behavior of the anomalous Hall conductivity and other effects that do not occur in previously studied systems.