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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. 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 $χ$. 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 $π/2$ in $χ$ exists between the $G-χ$ 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.