ArXiv · 2026
The observation of superconductivity emerging from a spin- and valley-polarized normal state in rhombohedral graphene raises a basic puzzle: intravalley Cooper pairs involve states that are not generically degenerate because of trigonal warping, and therefore lack the particle–particle nesting underlying the conventional Cooper instability. While recent model studies suggest that nontrivial band geometry can strongly promote chiral pairing, how this geometric enhancement competes with realistic band-structure-induced pair breaking remains unclear. Here we study Kohn–Luttinger superconductivity in electron-doped rhombohedral tetralayer graphene using a DFT-fitted multiorbital tight-binding model, retaining the full Bloch-wave-function form factors in both RPA screening and the projected Cooper interaction. We separate the superconducting instability into three contributions: the symmetry-resolved form-factor-dressed interaction, the Cooper-pair phase space determined by the symmetrized pair dispersion, and the energy mismatch generated by trigonal warping. We find that the Bloch form factors strongly favor intravalley pairing, with a leading predominantly pₓ-ip_y instability and a substantially larger maximum T_c than the intervalley reference state. At the same time, trigonal-warping-induced mismatch cuts off the Cooper logarithm and confines intravalley superconductivity to a much narrower region of the phase diagram. The dominant instability occurs near pair-Lifshitz transitions and primarily in reconstructed annular or three-lobed Fermi-surface regimes. Our results show that superconductivity in rhombohedral graphene is controlled by the combined effects of quantum-geometry-dressed interactions, pair fermiology, and trigonal-warping-induced pair breaking.
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