Isospin- and momentum-polarized orders in bilayer graphene

Abstract

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 moir\'e 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 ${K}^{\ensuremath{'}}$ 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.