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

Symmetry-broken correlated metals and superconductivity have recently been observed in rhombohedral trilayer graphene. Interestingly, superconductivity always occurs on the cusp of isospin symmetry breaking, indicating that the pairing glue may be provided by order parameter fluctuations. I will argue that the relevant symmetry broken state is inter-valley coherent (IVC), and that IVC fluctuations can lead to unconventional superconductivity which is chiral when the fluctuations are strong. Along the way, I will clarify the role of the inter-valley Hund's coupling in choosing the spin-structure of both the IVC phase and the superconductor, and find a natural explanation of an apparently puzzling feature in the experiments — the occurrence of spin-singlet superconductivity in close proximity of a spin-polarized metal.