Dirac quasiparticle tunneling in a NG/ferromagnetic barrier/SG graphene junction

We study the tunneling conductance in a spin dependent barrier NG/FB/SG graphene junction, where NG, FB and SG are normal graphene, gate ferromagnetic graphene barrier with thickness d and the graphene s-wave superconductor, respectively. In our work, the quasiparticle scattering process at the interfaces is based on quasi particles governed by the Dirac Bogoliubov–de Gennes equation with effective speed of light vF ∼ 106 m/s. The conductance of the junction is calculated based on Blonder–Tinkham–Klapwijk (BTK) formalism. The oscillatory conductance under varying gate potential and exchange energy in FB and the conductance induced by specular Andreev reflection are studied. By taking into account both effects of barrier strengths due to the gate potential χG∼VGd/ℏvFχG∼VGd/ℏvF and the exchange energy χex∼Eexd/ℏvFχex∼Eexd/ℏvF in the FB region, we find that the zero bias conductance of junction depends only on the ferromagnetic barrier strength χex in FB, when the Fermi energy in SG is very much larger than that the Fermi energy in NG (EFS ≫ EFN). The oscillatory conductance peaks can be controlled by either varying χex or χG. In the limiting case, by setting Eex = 0, the conductance in a NG/NB/SG graphene junction, where SG is the s-wave superconductor, is also studied in order to compare with two earlier contradicted data. Our result agrees with what was obtained by Linder and Sudbo [J. Linder, A. Sudbo, Phys. Rev. B 77 (2008) 64507], which confirms the contradiction to what was given by Bhattacharjee and Sengupta [S. Bhattacharjee, K. Sengupta, Phys. Rev. Lett. 97 (2006) 217001].