  Interaction-driven spontaneous symmetry breaking lies at the heart of many
quantum phases of matter. In moir\'e systems, broken spin/valley 'flavour'
symmetry in flat bands underlies the parent state out of which ultimately
correlated and topological ground states emerge. However, the microscopic
mechanism of such flavour symmetry breaking and its connection to the
low-temperature many-body phases remain to be understood. Here, we investigate
the symmetry-broken 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 a
pinning of the chemical potential $\mu$ at all integer fillings of the moir\'e
superlattice, highlighting 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 $C=3,2,1$ at filling
factors $\nu=1,2,3$, respectively, consistent with flavour symmetry breaking in
the Hofstadter's butterfly spectrum of MATBG. Moreover, our concurrent
measurements of resistivity and chemical potential allow us to obtain the
temperature dependence of the charge diffusivity of MATBG in the strange metal
regime, a quantity previously explored only in ultracold atom systems. Our
results bring us one step closer to a unified framework for understanding
interactions in the topological bands of MATBG, both in the presence and
absence of a magnetic field.
