Ohmic and non-Ohmic Andreev transport through an interface between superconductor and hopping insulator: Dramatic role of barrier properties

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At low temperatures and voltages tunneling transport through an interface between a superconductor and hopping insulator is dominated by coherent two-electron tunneling between the Cooper-pair condensate and pairs of localized states, see Kozub et al., PRL 96, 107004 (2006). By detailed analysis of such transport we show that the interface resistance is extremely sensitive to the properties of the tunneling barriers, as well as to asymptotic behavior of the localized states. In particular, dramatic cancellation takes place for hydrogen-like impurities and ideal barrier. However, some disorder can lift the cancellations restoring the interface transport. We also study non-Ohmic behavior of the interface resistor and show that it is sensitive to the Coulomb correlation of the occupation probabilities of the involved localized states. It is expected that non-Ohmic contribution to I-V-curve will experience pronounced mesoscopic (fingerprint) fluctuations.