Eur. Phys. J. B (2016) 89: 250
https://doi.org/10.1140/epjb/e2016-70428-4

Regular Article

Emergence of F(R) gravity-analogue due to defects in graphene

¹ Faculty of Physics, Shahid Bahonar University, P.O. Box 76175, Kerman, Iran
² Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), P.O. Box 55134 -441, Maragha, Iran
³ Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 043 53 Kosice, Slovak Republic
⁴ Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia
⁵ Netherlands Institute for Advanced Study, Korte Spinhuissteeg 3, 1012 CG Amsterdam, the Netherlands
⁶ Department of Physics, Faculty of Science, Benha University, Benha 13518, Egypt

^a e-mail: pincak@saske.sk

Received: 12 July 2016
Received in final form: 5 September 2016
Published online: 21 November 2016

Abstract

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.