In magic-angle twisted bilayer graphene (tBLG), the periodic moiré superlattice potential leads to extremely narrow electronic bands that support a variety of correlated phases. Further richness arises in the presence of a perpendicular magnetic field, where the interplay between moiré and magnetic length scales provides an opportunity to investigate Hofstadter butterfly physics in the presence of strong interactions. In this talk, I will describe local electronic compressibility measurements of tBLG in this regime conducted with a scanning single-electron transistor. Our data reveal a surprising sequence of correlated Chern insulators and multiple phase transitions between them, which reflect a delicate competition between single-particle Hofstadter subband energy gaps and many-body interactions. We experimentally extract the strongly correlated Hofstadter spectrum of tBLG and map out its phase diagram of flavor degeneracy/polarization as a function of density and magnetic field. I will discuss our results in the context of symmetry breaking terms and polarization of the quantum degrees of freedom.
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