Effect of vacancy defects on the Josephson current in zigzag graphene narrow strips

We investigate the Josephson current in a superconductor/zigzag graphene narrow strip/superconductor (Sc-ZGNS-Sc) junction, with vacancy defects. For this purpose, we extend a recursive Green’s function based numerical method to ZGNSs and take into account the effect of vacancies including random single vacancy distributions and also chain-like linear defects. We investigate how the Josephson current is affected by the length and the width of the strip and the concentration of the vacancies. We find that the Josephson current exhibits an exponentially dependence on the vacancy concentration. The exponent coefficient is a nonlinear function of the length of the lattice and the vacancy concentration. For the width dependence we find a linear relation between the Josephson current and the width of the ZGNS which propose a semi classical treatment of the electron transport in this system. Finally, we study the effect of chain-like linear defects and compare them with randomly distributed single vacancies.