Quantitative description of charge transport across tunneling and break-junction devices with novel superconductors encounters some problems not present, or not as severe for traditional superconducting materials. In this work, we explain unexpected features in related transport characteristics as an effect of a degraded nano-scaled sheath at the superconductor surface. Model capturing main aspects of the ballistic charge transport across hybrid superconducting structures with normally-conducting nm-thick interlayers is proposed. The calculations are based on a scattering formalism taking into account Andreev electron-into-hole (and inverse) reflections at normal metal-superconductor interfaces as well as transmission and backscattering events in insulating barriers between the electrodes. Current-voltage characteristics of such devices exhibit a rich diversity of anomalous (from the viewpoint of the standard theory) features, in particular, shift of differential-conductance maximums at gap voltages to lower positions and appearance of well-defined dips instead expected coherence peaks. We compare our results with related experimental data.
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