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

We study the tunneling conductance in a spin dependent barrier NG/F_B/SG graphene junction, where NG, F_B 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 v_F ∼ 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 F_B and the conductance induced by specular Andreev reflection are studied. By taking into account both effects of barrier strengths due to the gate potential χ_G∼V_Gd/?v_F${\chi }_{\text{G}}\sim V_{\text{G}}d/?v_{\text{F}}$ and the exchange energy χ_ex∼E_exd/?v_F${\chi }_{\text{ex}}\sim E_{\text{ex}}d/?v_{\text{F}}$ in the F_B region, we find that the zero bias conductance of junction depends only on the ferromagnetic barrier strength χ_ex in F_B, when the Fermi energy in SG is very much larger than that the Fermi energy in NG (E_FS ? E_FN). The oscillatory conductance peaks can be controlled by either varying χ_ex or χ_G. In the limiting case, by setting E_ex = 0, the conductance in a NG/N_B/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].