Generalization of Blonder-Tinkham-Klapwijk theory to particle-hole mixing boundary conditions: π-shift and conductance dips

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We generalize the Blonder-Tinkham-Klapwijk theory considering non-diagonal boundary conditions in the Bogoliubov-de Gennes scattering problem, to describe anomalous conductance features often reported for normal-metal/superconductor contacts. We calculate the differential conductance spectra showing that conductance dips, not expected in the standard formulation, are explained in terms of phase π-shift, between the bulk and the interface order parameter, possibly induced by a localized magnetic moment. A discretized model is used to give quantitative evaluation of the physical conditions, namely the polarization and transparency of the interface, needed to realize the phase gradient.