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

Abstract

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 ∼ 10 6 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 G d / ℏ v F and the exchange energy χ ex ∼ E ex d / ℏ v 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].