Physics

Bilayer graphene

Instability

Membrane

Ferromagnetism

Biology

Magnetic field

Vortex

Phase transition

Hall effect

Bilayer

Acoustics

Quantum Hall effect

Condensed matter physics

Lattice (music)

Graphene

Quantum mechanics

Anisotropy

Genetics

Thermodynamics

Physical Review Letters

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.

Mechanism for Anomalous Hall Ferromagnetism in Twisted Bilayer Graphene