Interaction-driven spontaneous symmetry breaking lies at the heart of many quantum phases of matter. In moiré systems, broken spin/valley ‘flavour’ symmetry in flat bands underlies the parent state from which correlated and topological ground states ultimately emerge^{1,2,3,4,5,6,7,8,9,10}. However, the microscopic mechanism of such flavour symmetry breaking and its connection to the low-temperature phases are not yet understood. Here we investigate the broken-symmetry many-body ground state of magic-angle twisted bilayer graphene (MATBG) and its nontrivial topology using simultaneous thermodynamic and transport measurements. We directly observe flavour symmetry breaking as pinning of the chemical potential at all integer fillings of the moiré superlattice, demonstrating the importance of flavour Hund’s coupling in the many-body ground state. The topological nature of the underlying flat bands is manifested upon breaking time-reversal symmetry, where we measure energy gaps corresponding to Chern insulator states with Chern numbers 3, 2, 1 at filling factors 1, 2, 3, respectively, consistent with flavour symmetry breaking in the Hofstadter butterfly spectrum of MATBG. Moreover, concurrent measurements of resistivity and chemical potential provide the temperature-dependent charge diffusivity of MATBG in the strange-metal regime¹¹—a quantity previously explored only in ultracold atoms¹². Our results bring us one step closer to a unified framework for understanding interactions in the topological bands of MATBG, with and without a magnetic field.

相互作用驱动的自发对称破缺是物质许多量子相的核心。在莫尔系统中，平带中破碎的自旋/谷“风味”对称性是最终出现相关和拓扑基态的母态的基础^{1,2,3,4,5,6,7,8,9,10}. 然而，这种风味对称性破坏的微观机制及其与低温相的联系尚不清楚。在这里，我们使用同时​​热力学和传输测量研究了魔角扭曲双层石墨烯 (MATBG) 的破缺对称多体基态及其非平凡拓扑。我们直接观察到风味对称性破坏是摩尔超晶格所有整数填充处化学势的钉扎，证明了风味 Hund 耦合在多体基态中的重要性。底层平带的拓扑性质在打破时间反转对称性时表现出来，我们分别在填充因子 1、2、3 处测量对应于陈数 3、2、1 的陈绝缘体状态的能隙，与 MATBG 的 Hofstadter 蝴蝶谱中的风味对称性破坏一致。此外，电阻率和化学势的同时测量提供了 MATBG 在奇异金属状态下的温度依赖性电荷扩散率^11——以前只在超冷原子中探索过的量¹²。我们的结果使我们更接近于理解 MATBG 拓扑带中相互作用的统一框架，无论有无磁场。