Tight-binding study of bilayer graphene Josephson junctions
  Using highly efficient simulations of the tight-binding Bogoliubov-de Gennes model we solved self-consistently for the pair correlation and the Josephson current in a Superconducting-Bilayer graphene-Superconducting Josephson junction. Different doping levels for the non-superconducting link are considered in the short and long junction regime. Self-consistent results for the pair correlation and superconducting current resemble those reported previously for single layer graphene except in the Dirac point where remarkable differences in the proximity effect are found as well as a suppression of the superconducting current in long junction regime. Inversion symmetry is broken by considering a potential difference between the layers and we found that the supercurrent can be switched if junction length is larger than the Fermi length. 
W. A. Mu\~noz, L. Covaci and F. M. Peeters
cond-mat.supr-con cond-mat.mes-hall