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 longrange 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 similar 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.