Quantum Geometry and Pair Breaking in Intra- and Intervalley Superconductivity of Rhombohedral Graphene

@misc{primeau2026quantum,
  title = {{Quantum Geometry and Pair Breaking in Intra- and Intervalley Superconductivity of Rhombohedral Graphene}},
  author = {Louis Primeau and Yang Zhang and Shi-Zeng Lin},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.14480},
  eprint = {2610.14480},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.14480},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Quantum Geometry and Pair Breaking in Intra- and Intervalley Superconductivity of Rhombohedral Graphene
AU  - Louis Primeau
AU  - Yang Zhang
AU  - Shi-Zeng Lin
PY  - 2026
DA  - 2026/10/10
PB  - arXiv
DO  - 10.48550/arxiv.2610.14480
UR  - https://arxiv.org/abs/2610.14480
AB  - 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 p_x−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.
ER  -