Transport properties of normal and ferromagnetic atomic-size constrictions with superconducting electrodes

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We present a theoretical approach to the transport properties of normal (N) and ferromagnetic (F) atomic-size contacts between superconducting (S) electrodes. This approach is based on non-equilibrium Green function techniques and a Hamiltonian description of the electron transfer processes in the constriction region. For a normal atomic-size contact the theory allows to relate the conduction channels to the atomic orbital structure. In the ferromagnetic case spin polarization gives rise to a spin dependent transmission distribution. For the case of S–N–S constrictions this theory predicts a d.c. current and shot noise in remarkable agreement with recent experimental results. We also analyze S–F and S–F–S constrictions. In this last case the current–voltage characteristic exhibits a very peculiar subgap structure associated to the competition between the multiple Andreev reflection mechanism and the ferromagnetic spin polarization.