Magic-angle twisted bilayer graphene (MATBG) exhibits a range of correlated phenomena that originate from strong electron–electron interactions. These interactions make the Fermi surface highly susceptible to reconstruction when ±1, ±2 and ±3 electrons occupy each moiré unit cell, and lead to the formation of various correlated phases^1,2,3,4. Although some phases have been shown to have a non-zero Chern number^5,6, the local microscopic properties and topological character of many other phases have not yet been determined. Here we introduce a set of techniques that use scanning tunnelling microscopy to map the topological phases that emerge in MATBG in a finite magnetic field. By following the evolution of the local density of states at the Fermi level with electrostatic doping and magnetic field, we create a local Landau fan diagram that enables us to assign Chern numbers directly to all observed phases. We uncover the existence of six topological phases that arise from integer fillings in finite fields and that originate from a cascade of symmetry-breaking transitions driven by correlations^7,8. These topological phases can form only for a small range of twist angles around the magic angle, which further differentiates them from the Landau levels observed near charge neutrality. Moreover, we observe that even the charge-neutrality Landau spectrum taken at low fields is considerably modified by interactions, exhibits prominent electron–hole asymmetry, and features an unexpectedly large splitting between zero Landau levels (about 3 to 5 millielectronvolts). Our results show how strong electronic interactions affect the MATBG band structure and lead to correlation-enabled topological phases.

魔角扭曲双层石墨烯（MATBG）表现出一系列源自强电子-电子相互作用的相关现象。当 ±1、±2 和 ±3 电子占据每个莫尔晶胞时，这些相互作用使费米表面极易重建，并导致形成各种相关相^1,2,3,4。尽管已显示某些阶段具有非零陈数^5,6，许多其他相的局部微观性质和拓扑特征尚未确定。在这里，我们介绍了一组技术，这些技术使用扫描隧道显微镜来绘制在有限磁场中出现在 MATBG 中的拓扑相。通过使用静电掺杂和磁场跟踪费米能级的局部态密度的演变，我们创建了一个局部朗道扇形图，使我们能够将陈数直接分配给所有观察到的相。我们揭示了六个拓扑相的存在，这些拓扑相由有限域中的整数填充引起，并且起源于由相关性驱动的一连串对称破缺跃迁^7,8. 这些拓扑相只能在魔角周围的小范围扭转角中形成，这进一步将它们与在电荷中性附近观察到的朗道能级区分开来。此外，我们观察到即使是在低场拍摄的电荷中性朗道光谱也因相互作用而显着改变，表现出显着的电子-空穴不对称性，并且在朗道零能级（约 3 至 5 毫电子伏特）之间具有出乎意料的大分裂。我们的结果显示了强电子相互作用如何影响 MATBG 能带结构并导致启用相关的拓扑相。