Cascade of electronic transitions in magic-angle twisted bilayer graphene

Magic-angle twisted bilayer graphene exhibits a variety of electronic states, including correlated insulators(1-3), superconductors(2-4)and topological phases(3,5,6). Understanding the microscopic mechanisms responsible for these phases requires determination of the interplay between electron-electron interactions and quantum degeneracy (the latter is due to spin and valley degrees of freedom). Signatures of strong electron-electron correlations have been observed at partial fillings of the flat electronic bands in recent spectroscopic measurements(7-10), and transport experiments have shown changes in the Landau level degeneracy at fillings corresponding to an integer number of electrons per moire unit cell(2-4). However, the interplay between interaction effects and the degeneracy of the system is currently unclear. Here we report a cascade of transitions in the spectroscopic properties of magic-angle twisted bilayer graphene as a function of electron filling, determined using high-resolution scanning tunnelling microscopy. We find distinct changes in the chemical potential and a rearrangement of the low-energy excitations at each integer filling of the moire flat bands. These spectroscopic features are a direct consequence of Coulomb interactions, which split the degenerate flat bands into Hubbard sub-bands. We find these interactions, the strength of which we can extract experimentally, to be surprisingly sensitive to the presence of a perpendicular magnetic field, which strongly modifies the spectroscopic transitions. The cascade of transitions that we report here characterizes the correlated high-temperature parent phase(11,12)from which various insulating and superconducting ground-state phases emerge at low temperatures in magic-angle twisted bilayer graphene. Electron-electron interactions in magic-angle twisted bilayer graphene can split usually degenerate electronic bands, giving rise to a cascade of electronic transitions revealed by spectroscopy.