Magnetic and Kohn-Luttinger instabilities near a Van Hove singularity: monolayer versus twisted bilayer graphene

TL;DR

This paper explores the competing electronic instabilities near Van Hove singularities in monolayer and twisted bilayer graphene, revealing dominant pairing in monolayers and ferromagnetic tendencies in twisted bilayers due to their distinct dispersion characteristics.

Contribution

It provides a comparative analysis of many-body instabilities in monolayer versus twisted bilayer graphene near Van Hove singularities, highlighting the different dominant orders.

Findings

Pairing instability dominates in monolayer graphene near Van Hove singularity.

Ferromagnetic instability becomes dominant in twisted bilayer graphene as the band flattens.

Electron pairing occurs in an extended f-wave channel with a nodal order parameter.

Abstract

We investigate the many-body instabilities of electrons interacting near Van Hove singularities arising in monolayer and twisted bilayer graphene. We show that a pairing instability must be dominant over the tendency to magnetic order as the Fermi level is tuned to the Van Hove singularity in the conduction band of graphene. As a result of the extended character of the saddle points in the dispersion, we find that the pairing of the electrons takes place preferentially in a channel of f-wave symmetry, with an order parameter vanishing at the position of the saddle points along the Fermi line. In the case of the twisted bilayers, the dispersion has instead its symmetry reduced down to the C_{3v} group and, most importantly, it leads to susceptibilities that diverge at the saddle points but are integrable along the Fermi line. This implies that a ferromagnetic instability becomes dominant in the twisted graphene bilayers near the Van Hove singularity, with a strength which is amplified as the lowest subband of the electron system becomes flatter for decreasing twist angle.