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We show that the superconducivity in twisted graphene multilayers originatesfrom a common feature, which is the strong valley symmetry breakingcharacteristic of these moir\'e systems at the magic angle. This leads to abreakdown of the rotational symmetry of the flat moir\'e bands down to $C_3$,and to ground states in which the time-reversal symmetry is broken for a givenspin projection. However, this symmetry can be recovered upon exchange ofspin-up and spin-down electrons, as we illustrate by means of a self-consistentmicroscopic Hartree-Fock resolution where the states for the two spinprojections acquire opposite sign of the valley polarization. There is then aspin-valley locking by which the Fermi lines for the two spin projections aredifferent and related by inversion symmetry. This effect represents a largerenormalization of the bare spin-orbit coupling of the graphene multilayers,lending protection to the superconductivity against in-plane magnetic fields.In the twisted bilayer as well as in trilayer and quadrilayer graphene, thepairing glue is shown to be given by the nesting between parallel segments ofthe Fermi lines which arise from the breakdown of symmetry down to $C_3$. Thisleads to a strong Kohn-Luttinger pairing instability, which is relevant untilthe Fermi line recovers gradually a more isotropic shape towards the bottom ofthe second valence band, explaining why the superconductivity fades away beyondthree-hole doping of the moir\'e unit cell.

Universal mechanism of Ising superconductivity in twisted bilayer, trilayer and quadrilayer graphene