Superconductivity from repulsive interactions in rhombohedral trilayer graphene: A Kohn-Luttinger-like mechanism

We study the emergence of superconductivity in rhombohedral trilayer graphene due purely to the long-range Coulomb repulsion. This repulsive-interaction-driven phase in rhombohedral trilayer graphene (RTG) is significantly different from those found in twisted bilayer and trilayer graphenes. In the latter case, the nontrivial momentum-space geometry of the Bloch wave functions contributes to an effective attractive electron--electron interaction; this allows for less modulated order parameters and for spin-singlet pairing. In RTG, we instead find spin-triplet superconductivity with critical temperatures up to ~0.15 K. The critical temperatures strongly depend on electron filling and peak where the density of states diverge. The order parameter shows a significant modulation within each valley pocket of the Fermi surface.