Electronic phases in twisted bilayer graphene at magic angles as a result of Van Hove singularities and interactions

The discovery of different phases as a result of correlations, especially in low-dimensional materials, has been always an exciting and fundamental subject of research. Recent experiments on twisted bilayer graphene have revealed reentrant unconventional superconductivity as a function of doping as well as a Mott-like insulating phase when the two layers are twisted with respect to each other at certain ``magic'' angles for doping, corresponding to two particles per moir\'e unit cell. In this paper, we propose a microscopic model that takes into account interactions and the Van Hove singularities in the density of states of twisted bilayer graphene at doping corresponding to one particle (ν=1) per moir\'e unit cell and study how superconductivity emerges. We identify the possible symmetry of the order parameter as s^±, while, if the intervalley coupling is negligible, the symmetry is s⁺⁺. In addition, we find and characterize the insulating region of the system as a region with a uniform charge instability where there is coexistence of the metallic and insulating phases.