# A mechanism for anomalous Hall ferromagnetism in twisted bilayer graphene

## TL;DR

This paper models the anomalous Hall effect in twisted bilayer graphene using a Landau level approach, revealing phase transitions and unique Chern band properties that differ from traditional quantum Hall ferromagnetism.

## Contribution

It introduces a lowest Landau level model capturing the anomalous Hall effect and predicts phase transitions and excitonic vortex lattice formation in twisted bilayer graphene.

## Key findings

- Phase transition from spin-valley polarized insulator to metal with increased bandwidth.
- Chern band structure prevents inter-valley coherent phases.
- Potential formation of excitonic vortex lattice at high interaction anisotropy.

## Abstract

We use a lowest Landau level model to study the recent observation of an anomalous Hall effect in twisted bilayer graphene. This effective model is rooted in the occurrence of Chern bands which arise due to the coupling between the graphene device and its encapsulating substrate. Our model exhibits a phase transition from a spin-valley polarized insulator to a partial or fully valley unpolarized metal as the bandwidth is increased relative to the interaction strength, consistent with experimental observations. In sharp contrast to standard quantum Hall ferromagnetism, the Chern number structure of the flat bands precludes an instability to an inter-valley coherent phase, but allows for an excitonic vortex lattice at large interaction anisotropy.