  Flat electronic bands can accommodate a plethora of interaction driven
quantum phases, since kinetic energy is quenched therein and electronic
interactions therefore prevail. Twisted bilayer graphene, near so-called the
"magic angles", features \emph{slow} Dirac fermions close to the
charge-neutrality point that persist up to high-energies. Starting from a
continuum model of slow, but strongly interacting Dirac fermions, we show that
with increasing chemical doping away from the charge-neutrality point, a
time-reversal symmetry breaking, valley pseudo-spin-triplet, topological $p+ip$
superconductor gradually sets in, when the system resides at the brink of an
anti-ferromagnetic ordering (due to Hubbard repulsion), in qualitative
agreement with recent experimental findings. The $p+ip$ paired state exhibits
quantized spin and thermal Hall conductivities, polar Kerr and Faraday
rotations. Our conclusions should also be applicable for other correlated
two-dimensional Dirac materials.
