Bilayer graphene

Mathematics

Graphene

Quantum mechanics

Quantum Hall effect

Condensed matter physics

Landau quantization

Magnetic field

Superlattice

Geometry

Chern class

Physics

Ferromagnetism

Nature Physics

When the twist angle between two layers of graphene is approximately 1.1°, interlayer tunnelling and rotational misalignment conspire to create a pair of flat bands1 that are known to host various insulating, superconducting and magnetic states when they are partially filled2–7. Most work has focused on the zero-magnetic-field phase diagram, but here we show that twisted bilayer graphene in a finite magnetic field hosts a cascade of ferromagnetic Chern insulators with Chern number ∣C∣ = 1, 2 and 3. The emergence of the Chern insulators is driven by the interplay of the moiré superlattice with the magnetic field, which endows the flat bands with a substructure of topologically non-trivial subbands characteristic of the Hofstadter butterfly8,9. The new phases can be accounted for in a Stoner picture10; in contrast to conventional quantum Hall ferromagnets, electrons polarize into between one and four copies of a single Hofstadter subband1,11,12. Distinct from other moiré heterostructures13–15, Coulomb interacti...

Hofstadter subband ferromagnetism and symmetry-broken Chern insulators in twisted bilayer graphene