Correlated metals and unconventional superconductivity in rhombohedral trilayer graphene: A renormalization group analysis

TL;DR

This study uses renormalization group analysis to explore electronic instabilities and superconductivity in rhombohedral trilayer graphene near Van Hove singularities, highlighting the influence of Fermi surface nesting and Coulomb interactions.

Contribution

It provides a detailed phase diagram of RTG showing how electric fields and Coulomb interactions determine electronic orders and pairing symmetries, with a focus on realistic long-range interactions.

Findings

Instabilities towards intervalley coherent metallic or superconducting phases.

Spin-singlet d-wave pairing favored at small displacement fields.

Spin-singlet i-wave pairing favored at larger displacement fields.

Abstract

Motivated by recent experimental observations of correlated metallic phases and superconductivity in rhombohedral trilayer graphene (RTG), we perform an unbiased study of electronic ordering instabilities in hole-doped RTG. Specifically, we focus on electronic states energetically proximate to Van Hove singularities (VHSs), where a large density of states promotes different interaction-induced symmetry-breaking electronic orders. To resolve the Fermi surface near VHSs, we construct a fermionic hot-spot model and demonstrate that a perpendicular electric field can tune different nesting structures of the Fermi surface. Subsequently, we apply a renormalization group analysis to describe the low-energy phase diagrams of our model under both short-range repulsive interactions as well as realistic (long-range) Coulomb interactions. Our analysis shows instabilities towards either intervalley coherent metallic phases or superconducting phases. The dominant pairing channel depends crucially on the nature of Fermi surface nesting -- repulsive Coulomb interaction favors spin-singlet $d$-wave pairing for relatively small displacement field and spin-singlet $i$-wave pairing for larger displacement field. We argue that the phase diagram of RTG can be well-understood by modeling the realistic Coulomb interaction as the sum of repulsive density-density interaction and ferromagnetic spin-triplet intervalley coherence (IVC) Hund's coupling, while phonon-mediated electronic interactions have a negligible effect on this system, in sharp contrast to twisted graphene multilayers.