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The discovery of different phases as a result of correlations, especially inlow-dimensional materials, has been always an exciting and fundamental subjectof research. Recent experiments on twisted bilayer graphene have revealedreentrant unconventional superconductivity as a function of doping as well as aMott-like insulating phase when the two layers are twisted with respect to eachother at certain "magic" angles for doping corresponding to two particles permoire unit cell. In this work we propose a microscopic model that takes intoaccount interactions and the van Hove singularities in the density of states ofthe twisted bilayer graphene at doping corresponding to one particle ($\nu$ =1)per moir\'{e} unit cell and study how superconductivity emerges. We identifythe possible symmetry of the order parameter as $s^{\pm}$, while if theinter-valley coupling is negligible the symmetry is $s^{++}$. In addition, wefind and characterise the insulating region of the system, as a region with auniform charge instability where there is coexistence of the metallic andinsulating phases.

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