Kohn-Luttinger superconductivity in twisted bilayer graphene

J. González, T. Stauber

Published 2018-07-03Version 1

We show that the recently observed superconductivity in twisted bilayer graphene (TBG) can be explained as a consequence of the Kohn-Luttinger (KL) instability which leads to an effective attraction between electrons with originally repulsive interaction. Usually, the KL instability takes place at extremely low energy scales, but in TBG, a doubling and subsequent strong hybridization of the van Hove singularity (vHS) in the electronic spectrum occurs as the magic angle is approached, leading to an unprecedented flatness of the saddle points in the highest valence band (VB) with almost perfect nesting between states belonging to different valleys. The highly anisotropic screening induces an effective attraction in a $p$-wave channel with odd parity under the exchange of the two disjoined patches of the Fermi line. We also predict charge and/or spin-density-wave instabilities, adjacent to the superconducting phase, for a critical Hubbard interaction (well) below the bandwidth of the highest VB, reflecting the fact that the regime of the ultra-flat vHS occurs at a slightly larger angle than the magic angle of the quasi-flat band regime.