Superconductivity and magnetism in the surface states of ABC-stacked multilayer graphene*

ABC-stacked multilayer graphene (ABC-MLG) exhibits topological surface flat bands with a divergent density of states, leading to many-body instabilities at charge neutrality. Here, we explore electronic ordering within a mean-field approach with full generic treatment of all spin-isotropic, two-site charge density and spin interactions up to next-nearest neighbor (NNN) sites. We find that surface superconductivity and magnetism are significantly enhanced over bulk values. We find spin-singlet s wave and unconventional NNN bond spin-triplet f wave to be the dominant superconducting pairing symmetries, both with a full energy gap. By establishing the existence of ferromagnetic intra-sublattice interaction, (J2 < 0) we conclude that the f-wave state is favored in ABC-MLG. We trace this distinctive surface behavior to the strong sublattice polarization of the surface flat bands. We also find competing ferrimagnetic order, fully consistent with density functional theory (DFT) calculations. The magnetic order interpolates between sublattice ferromagnetism and antiferromagnetism, but only with the ratio of the sublattice magnetic moments (R) being insensitive to the DFT exchange correlation functional. By constraining the interactions to the DFT R-value we establish the phase diagram and find f-wave superconductivity being favored for all weak to moderately strong couplings J2 and as long as J2 is a sufficiently large part of the full interaction mix. Gating ABC-MLG away from charge neutrality further enhances the f-wave state over the ferrimagnetic state, establishing ABC-MLG as a strong candidate for f-wave superconductivity.