Superconductivity in Graphene induced by the rotated layer

Abstract

We linearize the Hamiltonian for Graphene in the vicinity of the nodes and obtain a two dimensional Dirac massless Hamiltonian for each layer. Including the spin–orbit a mass is introduced. The attractive interaction is obtained as a result of rotation of one of the layer. The mass introduced gives rise to attraction for small angle rotation. Using the spinors representation in the vicinity of the nodal Dirac points the interactions are modified. The parity anomaly resulting from rotations modifies the “APS” index theorem of “Gravitational” “Chern Simons”. We show directly that the combination of rotation and projection of the spinors in the vicinity of the Dirac nodes are modified in such way, that a repulsive real space interaction, becomes attractive in the restricted momentum space, in certain directions. The chemical potential controls the behavior.