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

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 bands 1 that are known to host various insulating, superconducting and magnetic states when they are partially filled 2 – 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 butterfly 8 , 9 . The new phases can be accounted for in a Stoner picture 10 ; in contrast to conventional quantum Hall ferromagnets, electrons polarize into between one and four copies of a single Hofstadter subband 1 , 11 , 12 . Distinct from other moiré heterostructures 13 – 15 , Coulomb interactions dominate in twisted bilayer graphene, as manifested by the appearance of Chern insulating states with spontaneously broken superlattice symmetry at half filling of a C = −2 subband 16 , 17 . Our experiments show that twisted bilayer graphene is an ideal system in which to explore the strong-interaction limit within partially filled Hofstadter bands. In twisted bilayer graphene, the moiré potential, strong electron–electron interactions and a magnetic field conspire to split the flat band into topologically non-trivial subbands.