Superconductivity in Rhombohedral Trilayer Graphene: Quasiparticle Pairing within the Intervalley Coherent Phase

Superconductivity (SC) is observed in rhombohedral trilayer graphene (RTG) in a narrow regime between the flavor-symmetric state and the symmetry breaking phase, which cannot be described by the conventional BCS theory. The measured coherence length, for instance, is roughly two orders of magnitude shorter than the value predicted by the BCS relation based on the large fermi velocity and an extremely low charge carrier densities of the flavor-symmetric phase. To resolve the discrepancies, we propose that the RTG SC phase arises from the pairing of quasiparticles of the adjacent inter-valley coherent (IVC) state. We illustrate the SC behavior using gapped Dirac cones with the chemical potential $\mu$ close to the conduction band's bottom. 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 IVC quasiparticles, which is much suppressed compared to predictions from the BCS 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.