Superconductivity and magnetism in the surface states of ABC-stacked multilayer graphene

TL;DR

This paper investigates the emergence of surface superconductivity and magnetism in ABC-stacked multilayer graphene, revealing dominant surface $f$-wave pairing and magnetic orders driven by topological flat bands and specific interactions.

Contribution

It provides a comprehensive mean-field analysis of all relevant interactions, identifying surface $f$-wave superconductivity as the dominant phase and elucidating the role of sublattice polarization and magnetic order.

Findings

Surface $f$-wave superconductivity is favored at charge neutrality.

Surface magnetism can interpolate between ferromagnetic and antiferromagnetic orders.

Gating enhances $f$-wave superconductivity over magnetic states.

Abstract

ABC-stacked multilayer graphene (ABC-MLG) exhibits topological surface flat bands with a divergent density of states, leading to many-body instabilities at charge neutrality. Here, we explore electronic ordering within a mean-field approach with full generic treatment of all spin-isotropic, two-site charge density and spin interactions up to next-nearest neighbor (NNN) sites. We find that surface superconductivity and magnetism are significantly enhanced over bulk values. We find spin-singlet $s$ wave and unconventional NNN bond spin-triplet $f$ wave to be the dominant superconducting pairing symmetries, both with a full energy gap. By establishing the existence of ferromagnetic intra-sublattice interaction, $(J_2<0)$ we conclude that the $f$-wave state is favored in ABC-MLG, in sharp contrast to bulk ABC-graphite where chiral $d$- or $p$-wave states, together with s-wave states, display stronger ordering tendencies albeit not achievable at charge neutrality. We trace this distinctive surface behavior to the strong sublattice polarization of the surface flat bands. We also find competing ferrimagnetic order, fully consistent with density functional theory (DFT) calculations. The magnetic order interpolates between sublattice ferromagnetism and antiferromagnetism, but only with the ratio of the sublattice magnetic moments ($R$) being insensitive to the DFT exchange correlation functional. We finally establish the full phase diagram by constraining the interactions to the $R$-value identified by DFT. We find $f$-wave superconductivity being favored for all weak to moderately strong couplings $J_2$ and as long as $J_2$ is a sufficiently large part of the full interaction mix. Gating ABC-MLG away from charge neutrality further enhances the $f$-wave state over the ferrimagnetic state, establishing ABC-MLG as a strong candidate for $f$-wave superconductivity.