Flat-band ferromagnetism in twisted bilayer graphene

TL;DR

This paper applies a flat band ferromagnetism theorem to twisted bilayer graphene, predicting ferromagnetic ground states at specific fillings due to the irreducibility of the density matrix in the flat bands.

Contribution

It demonstrates that the flat band ferromagnetism theorem can be applied to TBG, predicting ferromagnetism at charge neutrality and half-filling based on the irreducibility of the density matrix.

Findings

Predicts ferromagnetic ground state at charge neutrality in TBG.

Shows ferromagnetism at half filling when a substrate-induced gap exists.

Validates the application of flat band ferromagnetism theorem to TBG.

Abstract

We discuss twisted bilayer graphene (TBG) based on a theorem of flat band ferromagnetism put forward by Mielke and Tasaki. According to this theorem, ferromagnetism occurs if the single particle density matrix of the flat band states is irreducible and we argue that this result can be applied to the quasi-flat bands of TBG that emerge around the charge-neutrality point for twist angles around the magic angle $\theta\sim1.05^\circ$. We show that the density matrix is irreducible in this case, thus predicting a ferromagnetic ground state for neutral TBG ($n=0$). We then show that the theorem can also be applied only to the flat conduction or valence bands, if the substrate induces a single-particle gap at charge neutrality. Also in this case, the corresponding density matrix turns out to be irreducible, leading to ferromagnetism at half filling ($n=\pm2$).