Josephson Current For a Graphene Nanoribbon Using a Lattice Model

A tight binding approach based on the Bogoliubov-de Gennes approach has been used to calculate the DC Josephson current for a lattice model for S-GNR-S junctions , for short junctions with respect to superconducting coherence length. We calculate the phase, length, width and chemical potential dependence at the Josephson junction and discuss the similarities and differences with regard to the theoretical and experimental results obtained for graphene. To make calculations on graphene, using a lattice model, we convert the graphene honeycomb structure to a brick lattice structure that does not change the lattice topology. Then, by removing several atoms from the lattice , we create the simple vacancy defects in the brick lattice and we also calculate Josephson current in the apparance of these vacancies .