Tunneling Charge Transport in Graphene-Based Superconductor Junctions

We study the spin polarized electron and hole tunneling transport through a graphene-based ferromagnet$(GF_1)$-insulator$(GI_1)$-superconductor$(G_{S})$-insulator$(GI_2)$-ferromagnet$(GF_2)$ junction. Proximity induced spin polarization and superconductivity in a graphene sheet are assumed to be created by superconducting and ferromagnetic electrodes placed on the top of the graphene. Using a four-dimensional version of the Dirac-Bogoliubov-de Gennes equation with appropriate boundary conditions we investigate the tunneling processes through the junctions. In particular, we present calculations of the amplitudes of normal and Andreev reflections as a function of the energy of the incident electron for a wide range of the model parameters, such as the strength and orientation of the exchange field, the barrier strength, and the distance between the two ferromagnetic layers. The tunneling transport processes in the graphene-based double junction GF/GI/$G_{S}$/GI/GF are compared with those in non-graphene-based junctions.