Kohn-Luttinger Superconductivity in Twisted Bilayer Graphene
J. González and T. Stauber
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 coupling of the van Hove singularities (vHS) in the electronic spectrum occurs as the magic angle is approached, leading to extended saddle points in the highest valence band 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 the appearance of a spin-density wave instability, adjacent to the superconducting phase, and the opening of a gap in the electronic spectrum from the condensation of spins with wave vector corresponding to the nesting vector close to the vHS.
(a) and (b) Density plot of the energy dispersion of the highest valence band E+k=max(EKk,EK′k) in the moiré Brillouin zone of the continuous model for two different twist angles. Dark (bright) colors represent high (low) energies and the black contour lines represent the Fermi surface at the energy of the van Hove singularity EvH. There occurs a doubling of the vHS at some critical angle θi=24>θ+c>θi=25, i.e., for lower θ there are twelve saddle points located inside the MBZ close to the lines that connect the Γ and K points. (c) and (d) Contour plot of the highest valence bands E+k and E−k of the tight-binding model for i=26. The two sets of vHS belonging to different valleys have already merged and are found now in different bands E+k and E−k.
