Spin and orbital metallic magnetism in rhombohedral trilayer graphene

We provide a theoretical interpretation of the metallic broken spin-valley (flavor) symmetry states recently discovered in hole-doped rhombohedral trilayer (ABC) graphene in large electric displacement fields. Our conclusions about the phase diagram and phase transitions combine insights from ABC graphene electronic structure models and mean-field theory, and are guided by the precise magneto-oscillation Fermi-surface-area measurements of recent experiments. We find that the principle of momentum-space condensation plays a key role in determining Fermi-surface reconstructions enabled by broken flavor symmetries when the single-particle bands imply thin annular Fermi seas. The reconstructed Fermi sea consists of one large outer Fermi-surface-enclosed majority-flavor states in reciprocal-space area Amaj and one or more small inner holelike Fermi-surface-enclosed minority-flavor states in Amin that are primarily responsible for nematic order. The competing ground states (valley-Ising, valley-XY, and spin-polarized state) have different Amaj/Amin and exchange energy maximizes this ratio and selects valley-XY nematic metal as the lowest-energy state. We discuss how the nematic pockets explain the observed fractionalization of quantum oscillation frequencies, and propose anisotropic transport and the nonlinear Hall effect as additional observables.