A mechanism for anomalous Hall ferromagnetism in twisted bilayer graphene

Understand

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.