Spontaneous orbital magnetization of the Wigner Crystal phase in Bernal bilayer graphene

At low density and low temperature, long-ranged Coulomb interactions in a two-dimensional electron gas cause the electrons to crystallize into a solid-like phase called a Wigner crystal(WC). In Bernal bilayer graphene, a perpendicular displacement field facilitates the formation of a WC by effectively flattening the bottom of the conduction band and thereby reducing the electrons' kinetic energy. Crucially, at a large displacement field, the conduction band adopts a "Mexican hat" shape, and this shape permits localized electrons to have finite angular momentum states that are nearly degenerate in energy with the ground state. Here we show that when the displacement field is larger than a certain critical value, Berry curvature drives the WC phase to be an orbital magnet with one unit of orbital angular momentum per electron. We calculate the corresponding phase diagram of the WC state, and we estimate its melting temperature and compressibility.