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 moiré 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 moiré 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.