Stoner ferromagnetism in low-angle twisted bilayer graphene at three-quarters filling

TL;DR

This paper theoretically explores how electron interactions in low-angle twisted bilayer graphene lead to ferromagnetism at three-quarters filling, aligning with recent experiments.

Contribution

It introduces a real-space recursion method combined with a Hubbard mean-field model to efficiently analyze magnetic properties in large twisted bilayer graphene systems.

Findings

Stoner ferromagnetism occurs at three-quarters filling in TBG.

Real-space recursion method efficiently handles large superlattices.

Results agree with previous momentum-space mean-field calculations.

Abstract

We present a theoretical investigation of the magnetic properties exhibited by twisted bilayer graphene (TBG) systems with small twist angles, where the appearance of flat minibands strongly enhances electron-electron interaction effects. We show that, at three-quarters filling of the conduction miniband, the Stoner mechanism induces a ferromagnetic polarization in the AA-stacking regions, which aligns with recent experimental observations. Our approach models the electronic properties by a tight-binding Hamiltonian combined with a Hubbard mean-field interaction term. We employ a real-space recursion technique to self-consistently calculate the system's local density of states and use our method to investigate the magnetic properties of small-angle TBG at three-quarters filling. The recursion method's $O({\cal N})$ efficiency makes it possible to address extremely large superlattices through a full real-space approach. We validate our procedure by comparing it with mean-field momentum-space calculations from the literature, which identify a magnetic phase in charge-neutral TBGs.