Kohn-Luttinger Superconductivity in Twisted Bilayer Graphene

We propose that the superconductivity observed in twisted bilayer graphene can be explained as the consequence of a Kohn-Luttinger instability, which leads to an effective attraction between electrons with originally repulsive interaction. As the first magic angle is approached, we find two consecutive transitions between different topologies in the highest valence band of the twisted bilayers, driven by the doubling and subsequent strong coupling of van Hove singularities in the electronic spectrum. This leads to extended saddle points and energy contours with almost perfect nesting between states belonging to different K valleys. The highly anisotropic screening of the Coulomb interaction induces an effective attraction in a channel with odd parity under the exchange of the two mirror patches of the Fermi line, which develop a universal shape close to the magic angle. We also consider the competition with charge and spin-density-wave instabilities, adjacent to the superconducting phase, and whose onset typically takes place for a Hubbard repulsion below the bandwidth of the highest valence band, thus reinforcing our microscopic approach to the superconductivity of twisted bilayer graphene.