Superconductivity in graphene induced by the rotated layer

Recent discoveries in graphene bilayers have revealed that when one of the layers is rotated by a specific angle, superconductivity emerges. We provide an explanation for this phenomenon. We find that due to the layer rotation the spinors and the nodal Dirac points also depend on the rotation angle. The combination of rotation and projection of the spinors in the vicinity of the two Dirac nodes is modified in such a way that a repulsive interaction becomes attractive in certain directions. The change from a repulsive interaction to an attractive one gives rise to a one-dimensional system described by the double sine-Gordon model for charge-density-waves and spin gap superconductivity. The competition between the two models is controlled by the chemical potential which acts as a bias field.