Tunneling conductance of graphene ferromagnet-insulator-superconductor junctions

We study the transport properties of a graphene ferromagnet-insulator-superconductor (FIS) junction within the Blonder-Tinkham-Klapwijk formalism by solving spin-polarized Dirac-Bogoliubov-de-Gennes equation. In particular, we calculate the spin polarization of tunneling current at the I-S interface and investigate how the exchange splitting of the Dirac fermion bands influences the characteristic conductance oscillation of the graphene junctions. We find that the retro- and specular Andreev reflections in the graphene FIS junction are drastically modified in the presence of exchange interaction and that the spin polarization (P-T) of tunneling current can be tuned from the positive to negative value by bias voltage (V). In the thin-barrier limit, the conductance G of a graphene FIS junction oscillates as a function of barrier strength chi. Both the amplitude and phase of the conductance oscillation varies with the exchange energy E-ex. For E-ex < E-F (Fermi energy), the amplitude of oscillation decreases with E-ex. For E-ex(c) > E-ex > E-F, the amplitude of oscillation increases with E-ex, where E-ex(c) = 2E(F) + U-0 (U-0 is the applied electrostatic potential on the superconducting segment of the junction). For E-ex > E-ex(c), the amplitude of oscillation decreases with E-ex again. Interestingly, a universal phase difference of pi/2 in chi exists between the G-chi curves for E-ex > E-F and E-ex < E-F. Finally, we find that the transitions between retro- and specular Andreev reflections occur at eV=|E-F-E-ex| and eV=E-ex+E-F, and hence the singular behavior of the conductance near these bias voltages results from the difference in transport properties between specular and retro-Andreev reflections.