Chiral Wigner crystal phases induced by Berry curvature

We study the impact of the Berry phase on the Wigner crystal (WC) state in a two-dimensional electron system. Using a model of Bernal bilayer graphene with a perpendicular displacement field, we show that the Berry curvature leads to a new type of WC state in which electrons acquire spontaneous orbital angular momentum once the displacement field exceeds a critical value. We determine the phase boundary of this WC state as a function of electron density and displacement field at low temperatures. We also derive the general effective Hamiltonian that describes the ordering of the electron spins and show that it contains a chiral term that can drive the system into chiral spin-density-wave or spin-liquid phases. The phenomena discussed here are directly relevant to the valley-polarized Wigner crystal phases observed in multilayer graphene.