Metals, fractional metals, and superconductivity in rhombohedral trilayer graphene

TL;DR

This paper investigates the superconducting and metallic states in rhombohedral trilayer graphene, revealing how doping, electric fields, and interactions lead to various correlated phases including spin-triplet and spin-singlet pairings, consistent with experiments.

Contribution

It combines mean-field and renormalization group analyses to elucidate the emergence of superconductivity and metallic states in doped rhombohedral trilayer graphene, highlighting the roles of interactions and external fields.

Findings

Identification of spin-triplet $f$-wave pairing near charge neutrality.

Discovery of isospin coherent paramagnetic state boosting $s$-wave pairing.

Explanation of the transition from half-metal to quarter-metal with doping.

Abstract

Combining mean-field and renormalization group analyses, here we unveil the nature of recently observed superconductivity and parent metallic states in chemically doped rhombohedral trilayer graphene, subject to external electric displacement fields ($D$) [H. Zhou, \emph{et al.}, Nature (London) {\bf 598}, 434 (2021)]. We argue that close to the charge neutrality, on site Hubbard repulsion favors layer antiferromagnet, which when combined with the $D$-field induced layer polarization, produces a spin-polarized, but valley-unpolarized half-metal, conducive to the nucleation of spin-triplet $f$-wave pairing (SC2). At larger doping valence bond order emerges as a prominent candidate for isospin coherent paramagent, boosting condensation of spin-singlet Cooper pairs in the $s$-wave channel (SC1), manifesting a "selection rule" among competing orders. Responses of these paired states to displacement and in-plane magnetic fields show qualitative similarities with experimental observation. With the onset of the quantum anomalous Hall order, the valley degeneracy of half-metal gets lifted, forming a quarter-metal at lower doping [H. Zhou, \emph{et al.}, Nature (London) {\bf 598}, 429 (2021)].