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

Coherent charge transport through an interface between a superconductor and hopping insulator: Role of barrier properties