Chern mosaic and Berry-curvature magnetism in magic-angle graphene

Charge carriers in magic-angle graphene come in eight flavours described by a combination of their spin, valley and sublattice polarizations. When inversion and time-reversal symmetries are broken, this ‘flavour’ degeneracy can be lifted, and their corresponding bands can be sequentially filled. Due to their non-trivial band topology and Berry curvature, each band is classified by a topological Chern number C, leading to quantum anomalous Hall and Chern insulator states. Using a scanning superconducting quantum interference device on a tip, we image the nanoscale equilibrium orbital magnetism induced by the Berry curvature, the polarity of which is governed by C, and detect its two constituent components associated with the drift and self-rotation of the electronic wavepackets. At integer filling v = 1, we observe a zero-field Chern insulator, which—rather than being described by a global topologically invariant C—forms a mosaic of microscopic patches of C = −1, 0 or 1. On further filling, we find a first-order phase transition due to the recondensation of electrons from valley K to K′, leading to irreversible flips of the local Chern number and magnetization, as well as to the formation of valley domain walls, giving rise to hysteretic anomalous Hall resistance. Topological states characterized by Chern numbers are usually considered to be the global properties of a material. Now a spatial patchwork of different Chern insulator states is imaged in twisted bilayer graphene.