Spin-valley locking and universal mechanism of Ising superconductivity in twisted bilayer, trilayer, and quadrilayer graphene

We show that the superconductivity in twisted bilayer, trilayer, and quadrilayer graphene originates from a common feature, which is the strong valley symmetry breaking characteristic of these moiré systems at the magic angle. This leads to a breakdown of the inversion symmetry of the flat moiré bands and to ground states with broken time-reversal symmetry for each spin projection. However, this symmetry can be recovered with the exchange of spin-up and spin-down electrons, as we illustrate by means of a self-consistent Hartree-Fock resolution where the two spin projections acquire opposite signs of the valley polarization. This implies a spin-valley locking in which the Fermi lines for spin-up and spin-down electrons are different and related by inversion symmetry, lending protection to the superconductivity against magnetic fields. In the twisted multilayers, the pairing glue is shown to be given by the nesting between parallel segments of the Fermi lines.This induces a strong Kohn-Luttinger instability, which is dominant until the Fermi level crosses the van Hove singularity in the second valence band. Then a Lifshitz transition occurs, leading to more isotropic Fermi lines and to a regime with vanishing pairing instability.