Spin-triplet superconductivity from inter-valley Goldstone modes in magic-angle graphene

TL;DR

This paper explores how inter-valley Goldstone modes in magic-angle graphene can mediate spin-triplet p-wave superconductivity, linking an inter-valley coherent insulator to neighboring superconducting phases.

Contribution

It demonstrates that Goldstone modes from symmetry breaking induce attractive interactions favoring spin-triplet pairing in magic-angle graphene.

Findings

Goldstone modes couple to charge carriers and mediate interactions.

The effective interaction favors spin-triplet p-wave superconductivity.

The leading instability is in the p-wave channel based on weak-coupling analysis.

Abstract

We consider magic-angle graphene in the doping regime around charge neutrality and study the connection between a recently proposed inter-valley coherent insulator at zero doping and the neighboring superconducting domes. The magic-angle graphene continuum model has an emergent U(1) valley-charge conservation symmetry, and an emergent SU(2) symmetry corresponding to opposite spin rotations in the two valleys. The inter-valley coherent insulator spontaneously breaks both these emergent symmetries, and as a result has four Goldstone modes which couple to doped charge carriers. We derive the effective interaction mediated by the Goldstone modes, and study its role in electron pair formation. The SU(2) Goldstone modes generate a ferromagnetic interaction, which is attractive in spin-triplet pairing channels and repulsive in spin-singlet channels. From a weak-coupling BCS calculation, we find the leading superconducting instability in the p-wave channel.