Inter-valley coherent order and isospin fluctuation mediated superconductivity in rhombohedral trilayer graphene

TL;DR

This paper investigates the role of inter-valley coherent order and isospin fluctuations in mediating unconventional superconductivity in rhombohedral trilayer graphene, revealing the influence of Hund's coupling on pairing symmetry.

Contribution

It demonstrates that inter-valley coherent fluctuations can induce chiral superconductivity and clarifies how Hund's coupling affects the spin structure of the superconducting state.

Findings

Inter-valley coherent fluctuations can mediate unconventional superconductivity.

Hund's coupling determines whether the pairing is spin-singlet or triplet.

Normal state spin polarization influences the pairing symmetry.

Abstract

Superconductivity was recently discovered in rhombohedral trilayer graphene (RTG) in the absence of a moir\'e potential. Superconductivity is observed proximate to a metallic state with reduced isospin symmetry, but it remains unknown whether this is a coincidence or a key ingredient for superconductivity. Using a Hartree-Fock analysis and constraints from experiments, we argue that the symmetry breaking is inter-valley coherent (IVC) in nature. We evaluate IVC fluctuations as a possible pairing glue, and find that they lead to chiral unconventional superconductivity when the fluctuations are strong. We further elucidate how the inter-valley Hund's coupling determines the spin-structure of the IVC ground state and breaks the degeneracy between spin-singlet and triplet superconductivity. Remarkably, if the normal state is spin-unpolarized, we find that a ferromagnetic Hund's coupling favors spin-singlet superconductivity, in agreement with experiments. Instead, if the normal state is spin-polarized, then IVC fluctuations lead to spin-triplet pairing.