Theory of magnetism and superconductivity in ABC trilayer graphene

The advent of moiré materials has led to unprecedent gate-tunable platforms for exploring topology, magnetism, superconductivity, and their interplay. Phase diagrams including Stoner-like half and quarter metals, spin-singlet and -triplet superconductors, and cascades of their phase transitions have been observed, first in the naturally occurring ABC-stacked trilayer graphene and later in AB-stacked bilayer graphene. Notably, all occurs in the absence of delicate moiré engineering, but under interplay between nonlinear Dirac bands and trigonal warping effects.Focusing on the trilayer graphene system, significant progress has been made by providing a theoretical framework that enables examination of the spontaneous spin-valley symmetry breaking and Fermi surface reconstructions observed in the fractional metallic phases and exploration of the tantalizing competitions between spin/orbital magnetism and singlet/triplet superconductivity. Specifically, the breaking of spin-valley symmetry is driven by momentum-space condensation that alters the Fermi surface topology from an annular disk to a circle and several crescents, by which the electrons can be compactly re-packed. This is consistent with the magneto-oscillation Fermi-surface-area measurements. Furthermore, the Cooper pairing can be generated by the repulsive Coulomb interaction, taking advantage of the large inter-pocket particle-hole susceptibility of an annular Fermi surface. In short, the inner and outer Fermi surfaces prefer d-wave spin-singlet and p-wave spin-triplet pairings, respectively. This allows not only elucidating the spin-singlet pairing observed at the present experiments but also predicting its transition to spin-triplet pairing. This framework [2] combining a Hartree-Fock mean-field theory and a functional renormalization group theory should turn out illuminating in understanding the collective behavior of correlated electrons in low-density, trigonally warped, few-layer graphene systems.