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Phenomenology of Andreev reflection from first-principles transport theory

We study Andreev reflection in normal metal-superconductor junctions by using an extended Blonder-Tinkham-Klapwijk model combined with transport calculations based on density functional theory. Starting from a parameter-free description of the underlying electronic structure, we perform a detailed investigation of normal metal-superconductor junctions, as the separation between the superconductor and the normal metal is varied. The results are interpreted by means of transverse momentum resolved calculations, which allow us to examine the contributions arising from different regions of the Brillouin zone. Furthermore we investigate the effect of a voltage bias on the normal metal-superconductor conductance spectra. Finally, we consider Andreev reflection in carbon nanotubes sandwiched between normal and superconducting electrodes.