▎ 摘　　要

When the twist angle between two layers of graphene is approximately 1.1 degrees, 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 divide C divide = 1, 2 and 3. The emergence of the Chern insulators is driven by the interplay of the moire 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 moire 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.