  We study one dimensional chains of superconducting islands with a particular
emphasis on the regime in which every second island is switched into its normal
state, thus forming a superconductor-insulator-normal metal (S-I-N) repetition
pattern. As is known since Giaever tunneling experiments, tunneling charge
transport between a superconductor and a normal metal becomes exponentially
suppressed, and zero-bias resistance diverges, as the temperature is reduced
and the energy gap of the superconductor grows larger than the thermal energy.
Here we demonstrate that this physical phenomenon strongly impacts transport
properties of inhomogeneous superconductors made of weakly coupled islands with
fluctuating values of the critical temperature. We observe a non-monotonous
dependence of the chain resistance on both temperature and magnetic field, with
a pronounced resistance peak at temperatures at which some but not all islands
are superconducting. We explain this phenomenon by the inhomogeneity of the
chains, in which neighboring superconducting islands have slightly different
critical temperatures. We argue that the Giaever's resistance divergence can
also occur in the zero-temperature limit. Such quantum transition can occur if
the magnetic field is tuned such that it suppresses superconductivity in the
islands with the weaker critical field, while the islands with stronger energy
gap remain superconducting. In such a field, the system acts as a chain of
S-I-N junctions.
