Kohn-Luttinger Superconductivity in Twisted Bilayer Graphene

TL;DR

This paper explains the superconductivity observed in twisted bilayer graphene as a Kohn-Luttinger instability driven by van Hove singularities and predicts a nearby spin-density wave phase.

Contribution

It demonstrates how enhanced van Hove singularities in TBG lead to effective p-wave attraction and predicts a spin-density wave instability adjacent to superconductivity.

Findings

Superconductivity in TBG can be explained by Kohn-Luttinger mechanism.

Effective p-wave pairing arises from anisotropic screening near vHS.

A spin-density wave phase is predicted near the superconducting region.

Abstract

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 (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 the appearance of a spin-density wave (SDW) 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.