Flavour Hund’s coupling, Chern gaps and charge diffusivity in moiré graphene

Interaction-driven spontaneous symmetry breaking lies at the heart of many quantum phases matter. In moir\'e systems, broken spin/valley 'flavour' in flat bands underlies parent state out which ultimately correlated and topological ground states emerge. However, microscopic mechanism such flavour its connection to low-temperature many-body remain be understood. Here, we investigate symmetry-broken magic angle twisted bilayer graphene (MATBG) nontrivial topology using simultaneous thermodynamic transport measurements. We directly observe as a pinning chemical potential $\mu$ all integer fillings superlattice, highlighting importance Hund's coupling state. The nature underlying is manifested upon time-reversal symmetry, where measure energy gaps corresponding Chern insulator with numbers $C=3,2,1$ filling factors $\nu=1,2,3$, respectively, consistent Hofstadter's butterfly spectrum MATBG. Moreover, our concurrent measurements resistivity allow us obtain temperature dependence charge diffusivity MATBG strange metal regime, quantity previously explored only ultracold atom systems. Our results bring one step closer unified framework for understanding interactions MATBG, both presence absence magnetic field.