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We study one dimensional chains of superconducting islands with a particularemphasis on the regime in which every second island is switched into its normalstate, thus forming a superconductor-insulator-normal metal (S-I-N) repetitionpattern. As is known since Giaever tunneling experiments, tunneling chargetransport between a superconductor and a normal metal becomes exponentiallysuppressed, and zero-bias resistance diverges, as the temperature is reducedand the energy gap of the superconductor grows larger than the thermal energy.Here we demonstrate that this physical phenomenon strongly impacts transportproperties of inhomogeneous superconductors made of weakly coupled islands withfluctuating values of the critical temperature. We observe a non-monotonousdependence of the chain resistance on both temperature and magnetic field, witha pronounced resistance peak at temperatures at which some but not all islandsare superconducting. We explain this phenomenon by the inhomogeneity of thechains, in which neighboring superconducting islands have slightly differentcritical temperatures. We argue that the Giaever's resistance divergence canalso occur in the zero-temperature limit. Such quantum transition can occur ifthe magnetic field is tuned such that it suppresses superconductivity in theislands with the weaker critical field, while the islands with stronger energygap remain superconducting. In such a field, the system acts as a chain ofS-I-N junctions.

Superconducting phase transition in inhomogeneous chains of superconducting islands