Correlated Hofstadter Spectrum and Flavor Phase Diagram in Magic Angle Graphene

In magic angle twisted bilayer graphene (MATBG), the moiré superlattice potential gives rise to narrow electronic bands which support a multitude of many-body quantum phases. Further richness arises in the presence of a perpendicular magnetic field, where the interplay between moiré and magnetic length scales leads to fractal Hofstadter subbands. In this talk, I will describe local electronic compressibility measurements of this strongly correlated Hofstadter platform conducted with a scanning single-electron transistor. By probing both gapped phases and the intervening compressible regimes, we simultaneously unveil novel sequences of broken-symmetry Chern insulators and resolve sharp phase transitions between competing states with different topological quantum numbers and spin/valley flavor occupations. Our measurements provide a complete experimental mapping of the energy spectrum and thermodynamic phase diagram of interacting Hofstadter subbands in MATBG. In addition, we observe full lifting of the degeneracy of the zeroth Landau levels together with level crossings, suggesting moiré valley splitting driven by mirror symmetry breaking. I will present a unified flavor polarization mechanism that accounts for the intricate interplay of topology, interactions, and symmetry breaking as a function of density and applied magnetic field in this system.