Rhombohedral Graphene: A Tale of Many Crystals

Abstract

Experiments on rhombohedral graphene have uncovered an extraordinary wealth of correlated quantum phases - from chiral superconductors to electronic crystals - all within a single family of atomically thin materials. Here, we introduce a simple indicator, derived from the noninteracting band dispersion, that identifies strongly correlated regions in the phase diagram of rhombohedral graphene as a function of carrier density and displacement field. We develop a neural-network variational Monte Carlo method, combined with Hartree-Fock theory, to solve the interacting ground states. Our calculation reveals a variety of electron crystals with no classical analog. These include, at increasing density: Wigner crystal, self-doped Wiger crystal, as well as ''anticrystal'', a lattice of holes in an electron liquid. We discuss their experimental manifestations and possible connection to superconductivity.