Unconventional superconductivity in nearly flat bands in twisted bilayer graphene

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.