Alejandro Jimeno Pozo

We theoretically explore the emergence of superconductivity arising from the Kohn-Luttinger mechanism due to Coulomb repulsion in non-twisted few layers of graphene. We employ the RPA approximation to account for the renormalization of the interacting potential and analyze how strong are the contributions from electron-electron and electron-phonon interactions. It seems that the purely electronic correlations are enough to give rise to a superconducting phase consistent with experimental measurements for Bernal bilayer and Rhombohedral trilayer graphene, and allows us to predict superconductivity in other stackings and configurations of few layers of graphene. The superconducting order parameter changes sign between valleys, indicating a valley-singlet, spin-triplet superconductivity in all graphene structures considered in this work. Additionally, the inclusion of Ising spin-orbit coupling leads to a significant enhancement in the critical temperature, as well as, it accounts for the broadening of the superconducting dome, also in line with experimental measurements.