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

Abstract

We present a theoretical study of the quasiparticle and subgap conductance of generic $X/{I}_{\text{sf}}/{S}_{M}$ junctions with a spin-filter barrier ${I}_{\text{sf}}$, 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 is 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 $N/{I}_{\text{sf}}/S$ junction, where $S$ is a conventional superconductor. In order to account for the spin-filter effect at interfaces, we heuristically derive boundary conditions for the quasiclassical Green's functions. With the help of these boundary conditions, we show that the proximity effect and the subgap conductance are suppressed by spin filtering in a $N/{I}_{\text{sf}}/S$ junction. Our work provides useful tools for the study of spin-polarized transport in hybrid structures both in the normal and in the superconducting state.