The nature of correlations in the insulating states of twisted bilayer graphene

The recently observed superconductivity in twisted bilayer graphene emerges from insulating states believed to arise from electronic correlations. In order to clarify the nature of such correlations we have analyzed the two-orbital Hubbard model in the honeycomb Moir\'e lattice with a slave spin technique. In this model, Mott states arise from local correlations at quarter- and half-fillings. Quarter-filling would correspond to the filling around which superconductivity has been observed in these systems. We show that the theoretical expectations from local correlations are not compatible with the experimentally observed behaviour of the insulating states with temperature and magnetic field. We argue that the inclusion of non-local correlations can reverse the predictions for the magnetic and temperature dependencies. Consequences for the critical interactions and possible pseudogap physics are also discussed.