  We show that the defects of graphene, which lead to the non-equality between
positive curvature of fermions with anti-parallel spins and negative curvature
of fermions with parallel spins, imply an emergence of F(R) gravity. By
increasing the number of atoms at each defect, the order of scalar curvature
increases and the shape of F(R) gravity changes. This gravity has a direct
relation with energy-momentum tensor and leads to motion of electrons in a
special path and hence producing superconductivity. Also, for some special
angles, parallel spins become close to each other and repel to each other. In
that condition, the shape of F(R) gravity changes and electrons can't continue
to move in an initial path and return. Consequently, superconductivity
disappears and one new conductivity appears in opposite direction.
