Unconventional superconductivity in nearly flat bands in twisted bilayer graphene

Bitan Roy, Vladimir Juricic

Published 2018-03-29, updated 2018-05-23Version 2

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 (CNP) and \emph{nearly} flat minibands around $1/4$ and $3/4$ fillings, which have also been observed in recent experiments. Starting from a continuum model of \emph{slow} Dirac fermions, we show that with increasing chemical doping away from the CNP, a \emph{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 strong Hubbard repulsion), in qualitative agreement with experimental findings. The $p+ip$ paired state exhibits quantized spin and thermal Hall conductivities, polar Kerr and Faraday rotations. Our conclusion may also be operative within the minibands around $1/4$ or $3/4$ filling if they can be described in terms of slow Dirac fermions.