  We argue that doped twisted bilayer graphene with magical twist angle can
become superconducting. In our theoretical scenario, the superconductivity
coexists with the spin-density-wave-like ordering. Numerical mean-field
analysis demonstrates that the spin-density-wave order, which is much stronger
than the superconductivity, leaves parts of the Fermi surface ungapped. This
Fermi surface serves as a host for the superconductivity. Since the magnetic
texture at finite doping breaks the point group of the twisted bilayer
graphene, the stabilized superconducting order parameter is nematic. We also
explore the possibility of a purely Coulomb-based mechanism of
superconductivity in the studied system. The screened Coulomb interaction is
calculated within the random phase approximation. It is shown that near the
half-filling the renormalized Coulomb repulsion indeed induces the
superconducting state, with the order parameter possessing two nodes on the
Fermi surface. We estimate the superconducting transition temperature, which
turns out to be very low. The implications of our proposal are discussed.
