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Electronic transport through ferromagnetic and superconducting junctions with spin-filter tunneling barriers

We present a theoretical study of the quasiparticle and subgap conductance of generic $X/I_{sf}/S_{M}$ junction with a spin-filter barrier $I_{sf}$, where $X$ is either a normal $N$ or a ferromagnetic metal $F$ and $S_{M}$ is a superconductor with a built-in exchange field. Our study is based on the tunneling Hamiltonian and the Green's function technique. First, we focus on the quasiparticle transport, both above and below the superconducting critical temperature. We obtain a general expression for the tunneling conductance which are valid for arbitrary values of the exchange field and arbitrary magnetization directions in the electrodes and in the spin-filter barrier. In the second part we consider the subgap conductance of a normal metal-superconductor junction with a spin-filter barrier. We provide a heuristic derivation of new boundary conditions for the quasiclassical Green's functions which take into account the spin-filter effect at the interface. With the help of these boundary conditions, we show how the proximity effect and the subgap conductance is suppressed by spin-filtering in a $N/I_{sf}/S$ junction, where $N$ is a normal metal. Our work provides useful tools for the study of spin-polarized transport in hybrid structures both in the normal and the superconducting state.