LAUSR

Abstract We linearize the Hamiltonian for Graphene in the vecinity of the nodes and obtain a two dimensional Dirac massles Hamiltonian for each layer. Including the spin–orbit a mass is introduced. The attractive interaction is obtain as a result of rotationof one of the layer. The mass introduced gives rise to attraction for small angle rotation. Using the spinors repesentation in the vecinity of the nodal Dirac points the inteactions are modified. The parity anomaly resulting from rotations modifies the “ A P S ” i n d e x theorem of “Gravitational” “Chern Simons”. We show directly that the combination of rotation and projection of the spinors in the vecinity 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 contoles the behavior.