Theory of Superconductivity in Magic-Angle Twisted Bilayer Graphene

Superconductivity in graphene bilayers occurs at certain "magic angles" of relative orientation between the layers. At these angles, the Moire-Bloch bandstructure becomes nearly flat at the Fermi energy. To describe superconductivity in these flat-band graphene bilayers, we extend the theory of superconductivity previously developed for single-layer graphene doped away from the Dirac point to the saddle point in the bandstructure on the edge of the Brillouin zone. The dominant channel for condensation is still spin-singlet Cooper pairing with d_x+id_y pair wavefunction, as we show using a perturbative renormalization group argument. Going beyond perturbation theory, we compute the entanglement spectrum using the Bardeen-Cooper-Schrieffer wavefunction and compare the result to the spectrum expected from the conformal field theory of a pair of free massless chiral Majorana fermions confined to the edge.