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 $A_{\text{maj}}$ and one or more small inner holelike Fermi-surface-enclosed minority-flavor states in $A_{\text{min}}$ that are primarily responsible for nematic order. The competing ground states (valley-Ising, valley-XY, and spin-polarized state) have different $A_{\text{maj}}/A_{\text{min}}$ 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.

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• Magnetic order
• Nematic order
• Graphene
• Two-dimensional electron system
• Fermi liquid theory
• Magnetism
• Mean field theory
• Variational wave functional methods