Phonon or electronic pairing in rhombohedral trilayer and Bernal bilayer graphene
In plain words
Graphene with three layers in staircase stacking, and ordinary two-layer graphene, superconduct at very low electron densities without any moire pattern, and it is disputed whether lattice vibrations or electron interactions cause the pairing.
Precise statement
Rhombohedral trilayer graphene superconducts with $T_{c}$ up to about 100 mK next to isospin-symmetry-breaking transitions (Zhou et al., Nature, 2021, doi:10.1038/s41586-021-03926-0), and Bernal bilayer graphene superconducts under in-plane magnetic field or with spin-orbit coupling induced by an adjacent WSe2 layer. Determine whether pairing is mediated by acoustic phonons (Chou et al., PRL 127, 187001, 2021) or by isospin fluctuations or Kohn-Luttinger repulsion (e.g., Chatterjee et al., Nature Communications, 2022, doi:10.1038/s41467-022-33561-w). An answer reproduces $T_{c}(n,D)$ in both systems and predicts the response to gate screening.
What would settle it
$T_{c}$ measured in devices with different gate-to-sample distances (screening suppresses electronic but not phonon pairing), compared with parameter-free calculations of both mechanisms.
Status in the literature
Unverified note
Phonon and electronic theories both remain in use as of 2026.