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.

魔角石墨烯中的电荷载流子有八种类型，由它们的自旋、谷和亚晶格极化组合描述。当反转和时间反转对称性被打破时，这种“风味”退化可以被解除，并且它们相应的带可以被顺序填充。由于它们的非平凡能带拓扑和贝里曲率，每个能带都由拓扑陈数C分类，导致量子反常霍尔和陈绝缘体状态。使用尖端上的扫描超导量子干涉装置，我们对由贝里曲率引起的纳米级平衡轨道磁性进行成像，其极性由C控制，并检测其与电子波包的漂移和自转相关的两个组成部分。在整数填充v  = 1 时，我们观察到零场 Chern 绝缘体，而不是由全局拓扑不变C描述 - 形成C  = -1、0 或 1的微观斑块的马赛克。在进一步填充时，我们发现由于电子从谷 K 到 K' 的再凝聚导致的一阶相变，导致局部陈数和磁化强度的不可逆翻转，以及谷畴壁的形成，从而产生迟滞异常霍尔电阻.