Electron bands in Bernal bilayer graphene flatten out in a transverse electric field, offering a promising platform for correlated electron physics. We discuss the spin/valley isospin magnetism resembling that seen in moiré bands. We predict that the isospin magnetism coexists with momentum-polarized phases occurring via a “flocking transition” in momentum space in which the electron distribution is spontaneously displaced in momentum space relative to the $K$ and $K^{\prime }$ valley centers. The momentum-polarized phases feature electronic nematicity manifest in the anisotropy of transport, and unusual observables such as persistent currents in the ground state. Momentum-polarized carriers “sample” the Berry curvature of the conduction band, resulting in a longitudinal and anomalous Hall conductivity that displays switching upon the flocking transition and other effects that do not occur in previously studied systems.

• Received 25 December 2022
• Accepted 12 January 2023

DOI:https://doi.org/10.1103/PhysRevB.107.075108