Intravalley spin-polarized superconductivity in rhombohedral tetralayer graphene

TL;DR

This paper models intravalley spin-polarized superconductivity in rhombohedral tetralayer graphene, showing it can emerge near Van Hove singularities with specific pairing symmetries, and aligns with experimental observations.

Contribution

It introduces a minimal anisotropic interaction model explaining superconductivity without Fermi surface nesting, identifying possible pairing states and their threshold conditions.

Findings

Superconductivity appears near Van Hove singularities.

Possible pairing states include $p+ip$, $h+ih$, and nodal $f$-wave.

Superconducting region has a narrow stripe shape, matching experiments.

Abstract

We study the intravalley spin-polarized superconductivity in rhombohedral tetralayer graphene, which has been discovered experimentally in Han $et$ $al$ arXiv:2408.15233. We construct a minimal model for the intravalley spin-polarized superconductivity, assuming a simplified anisotropic interaction that depends only on the angle between the incoming and outgoing momenta. Despite the absence of \textit{Fermi surface nesting}, we show that superconductivity can emerge near the Van Hove singularity with the maximal $T_c$ near a bifurcation point of the peaks in the density of states. We identify the $p+ip$, $h+ih$, and the nodal $f$-wave pairings as the possible states, which are all pair density wave orders due to the intravalley nature. Furthermore, these pair density wave orders require a finite attractive threshold for superconductivity, resulting in {a narrow stripe shape of superconducting region}, consistent with experimental findings. We point out that the Kohn-Luttinger mechanism is a plausible explanation with a dominant $p+ip$ pairing. The possibility of realizing intravalley spin-polarized superconductivity in other rhombohedral graphene systems is also discussed.