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

Abstract

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 $\hat{I}¼$ close to the valence band's edge. Our findings indicate that the transition temperature $T_c$ obeys $T_c\propto \hat{I}{\mu }_D\exp (-2/\ddot{I}{}_{\mathrm{qp}}U)$ with the density of states $\ddot{I}{}_{\mathrm{qp}}$ of intervalley coherent state quasiparticles, which is much suppressed compared to predictions from the Bardeen-Cooper-Schrieffer theory. The coherence length $\hat{I}¾$ we predict behaves according to $\hat{I}¾\sim v/\sqrt{\hat{I}¼T_c}$ 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 $\hat{I}¾$ without parameter fine-tuning.

11+17 pages, 3+1 diagrams, 2 tables, supplementary included