Valley magnetism, nematicity, and density wave orders in twisted bilayer graphene

TL;DR

This paper investigates various density-wave and Pomeranchuk orders in twisted bilayer graphene near Van Hove points, identifying key magnetic and nematic instabilities through a patch model analysis.

Contribution

It provides a detailed analysis of particle-hole instabilities and identifies two main candidate orders, including a robust ferromagnetic state and a complex spin-charge order, in twisted bilayer graphene.

Findings

Identification of SU(2)-breaking ferromagnetic order within a valley.

Discovery of a mixed 120° spin and orthogonal charge order.

Detection of attractive interactions in nematic channels.

Abstract

We analyze density-wave and Pomeranchuk orders in twisted bilayer graphene. This compliments our earlier analysis of the pairing instabilities. We assume that near half-filling of either conduction or valence band, the Fermi level is close to Van Hove points, where the density of states diverges, and study potential instabilities in the particle-hole channel within a patch model with two valley degrees of freedom. The hexagonal symmetry of twisted bilayer graphene allows for either six or twelve Van Hove points. We consider both cases and find the same two leading candidates for particle-hole order. One is an SU(2)-breaking spin state with ferromagnetism within a valley. A subleading inter-valley hopping induces antiferromagnetism between the valleys. The same state has also been obtained in strong coupling approaches, indicating that this order is robust. The other is a mixed state with $120^\circ$ complex spin order and orthogonal complex charge order. In addition, we find a weaker, but still attractive interaction in nematic channels, and discuss the type of a nematic order.