  We consider the superconducting and Mott-insulating states for the twisted
bilayer graphene, modeled as two narrow-band system of electrons with
appreciable intraatomic Coulomb interactions. The interaction induces kinetic
exchange which leads to real-space, either triplet- or singlet-spin pairing, in
direct analogy to heavy-fermions and high-temperature superconductors. By
employing the statistically-consistent Gutzwiller method, we construct
explicitly the phase diagram as a function of electron concentration for the
spin-triplet $d_{x^2 - y^2}+id_{xy}$ paired case, as well as determine the
topological edge states. The model reproduces principal features observed
experimentally in a semi-quantitative manner. The essential role of electronic
correlations in driving both the Mott-insulating and superconducting
transitions is emphasized. The transformation of the spin-triplet state into
its spin-singlet analogue is also analyzed, as well as the appearance of the
phase separated superconducting+Mott-insulating state close to the half
filling.
