Emergence of F(R) gravity-analogue due to defects in graphene
  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. 
Alireza Sepehri, Richard Pincak, Ahmed Farag Ali
cond-mat.mes-hall gr-qc math-ph math.MP