Correlated Hofstadter Spectrum and Flavor Phase Diagram in Magic Angle Graphene

Understand

In magic angle twisted bilayer graphene (MATBG), the moir\'e superlattice potential gives rise to narrow electronic bands1 which support a multitude of many-body quantum phases.

• Further richness arises in the presence of a perpendicular magnetic field, where the interplay between moir\'e and magnetic length scales leads to fractal Hofstadter subbands.
• In this strongly correlated Hofstadter platform, multiple experiments have identified gapped topological and correlated states, but little is known about the phase transitions between them in the intervening compressible regimes.
• Here, using a scanning single-electron transistor microscope to measure local electronic compressibility, we simultaneously unveil novel sequences of broken-symmetry Chern insulators (CIs) and resolve sharp phase transitions between competing states with different topological quantum numbers and spin/valley flavor occupations.