Superconductivity from Quasiparticle Pairing of Intervalley Coherent State in Rhombohedral Trilayer Graphene

Superconductivity is observed in rhombohedral trilayer graphene in a narrow regime between the flavor-symmetric state and the symmetry breaking phase, which cannot be described by the conventional Bardeen-Cooper-Schrieffer theory. The measured coherence length, for instance, is roughly two orders of magnitude shorter than the value predicted by the Bardeen-Cooper-Schrieffer relation based on the large fermi velocity and an extremely low charge carrier density of the flavor-symmetric phase. To resolve the discrepancies, we propose that the rhombohedral trilayer graphene superconducting phase arises from the pairing of quasiparticles of the adjacent inter-valley coherent state. We illustrate the superconducting phenomenology using gapped Dirac cones with the chemical potential $\mu$ close to the valence band's edge. Our findings indicate that the transition temperature $T_c$ obeys $T_c\propto \epsilon_D\exp(-2/\rho_\mathrm{qp}U)$ with the density of states $\rho_\mathrm{qp}$ of intervalley coherent state quasiparticles, which is much suppressed compared to predictions from the Bardeen-Cooper-Schrieffer theory. The coherence length $\xi$ we predict behaves according to $\xi\sim v/\sqrt{\mu T_c}$ with $v$ being the velocity of Dirac cone. Applying our assumption to a microscopic model, our predictions align well with experimental data and effectively capture key measurable quantities such as the transition temperature $T_c$ and the coherence length $\xi$ without parameter fine-tuning.