Ising superconductivity induced from spin-selective valley symmetry breaking in twisted trilayer graphene

TL;DR

This paper demonstrates that electron-electron interactions induce valley symmetry breaking in twisted trilayer graphene, leading to spin-valley locking and intrinsic spin-orbit coupling that protect superconductivity against magnetic fields, aligning with experimental observations.

Contribution

It reveals a novel mechanism of Ising superconductivity driven by spin-selective valley symmetry breaking in twisted trilayer graphene.

Findings

Valley symmetry is broken for each spin channel due to electron interactions.

Spin-valley locking causes Cooper pairs to form across opposite valleys.

Superconductivity is protected against in-plane magnetic fields by effective intrinsic spin-orbit coupling.

Abstract

We show that the $e$-$e$ interaction induces a strong breakdown of valley symmetry for each spin channel in twisted trilayer graphene, leading to a ground state where the two spin projections have opposite sign of the valley symmetry breaking order parameter. This leads to a spin-valley locking in which the electrons of a Cooper pair are forced to live on different Fermi lines attached to opposite valleys. Furthermore, we find an effective intrinsic spin-orbit coupling explaining the protection of the superconductivity against in-plane magnetic fields. The effect of spin-selective valley symmetry breaking is validated as it reproduces the experimental observation of the reset of the Hall density at 2-hole doping. It also implies a breakdown of the symmetry of the bands from $C_6$ to $C_3$, with an enhancement of the anisotropy of the Fermi lines which is at the origin of a Kohn-Luttinger (pairing) instability. The isotropy of the bands is gradually recovered, however, when the Fermi level approaches the bottom of the second valence band, explaining why the superconductivity fades away in the doping range beyond 3 holes per moir\'e unit cell in twisted trilayer graphene.