Print Email Facebook Twitter Spin-dependent boundary conditions for isotropic superconducting Green’s functions Title Spin-dependent boundary conditions for isotropic superconducting Green’s functions Author Cottet, A. Huertas-Hernando, D. Belzig, W. Nazarov, Y.V. Faculty Applied Sciences Department Kavli Institute of Nanoscience Date 2009-11-23 Abstract The quasiclassical theory of superconductivity provides the most successful description of diffusive heterostructures comprising superconducting elements, namely, the Usadel equations for isotropic Green’s functions. Since the quasiclassical and isotropic approximations break down close to interfaces, the Usadel equations have to be supplemented with boundary conditions for isotropic Green’s functions (BCIGF), which are not derivable within the quasiclassical description. For a long time, the BCIGF were available only for spin-degenerate tunnel contacts, which posed a serious limitation on the applicability of the Usadel description to modern structures containing ferromagnetic elements. In this paper, we close this gap and derive spin-dependent BCIGF for a contact encompassing superconducting and ferromagnetic correlations. This finally justifies several simplified versions of the spin-dependent BCIGF, which have been used in the literature so far. In the general case, our BCIGF are valid as soon as the quasiclassical isotropic approximation can be performed. However, their use requires the knowledge of the full scattering matrix of the contact, an information usually not available for realistic interfaces. In the case of a weakly polarized tunnel interface, the BCIGF can be expressed in terms of a few parameters, i.e., the tunnel conductance of the interface and five conductancelike parameters accounting for the spin dependence of the interface scattering amplitudes. In the case of a contact with a ferromagnetic insulator, it is possible to find explicit BCIGF also for stronger polarizations. The BCIGF derived in this paper are sufficiently general to describe a variety of physical situations and may serve as a basis for modeling realistic nanostructures. To reference this document use: http://resolver.tudelft.nl/uuid:5e52674a-429f-466d-a29a-4ab2ebfa8590 Publisher American Physical Society ISSN 0163-1829 Source Physical Review B, 80 (18), 2009 Part of collection Institutional Repository Document type journal article Rights (c) 2009 The Authors ; American Physical Society Files PDF Nazarov_2009.pdf 472.88 KB Close viewer /islandora/object/uuid:5e52674a-429f-466d-a29a-4ab2ebfa8590/datastream/OBJ/view