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 flavour-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 flavour-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 μ close to the valence band's edge. Our findings indicate that the transition temperature T_c obeys $T_c\propto {ϵ}_D\exp \left(-2/{\rho }_{\mathrm{qp}}U\right)$ with the density of states ρ_qp of intervalley coherent state quasiparticles, which is much suppressed compared to predictions from the Bardeen-Cooper-Schrieffer theory. The coherence length ξ we predict behaves according to $\xi ~v/\sqrt{\mu T_c}$ 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 ξ `without parameter fine-tuning.