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We have made a systematic investigation of charge transport in 1D chains ofJosephson junctions where the characteristic Josephson energy is much less thanthe single-island Cooper-pair charging energy, $E_\mathrm{J}\ll E_{CP}$. Suchchains are deep in the insulating state, where superconducting phase coherenceacross the chain is absent, and a voltage threshold for conduction is observedat the lowest temperatures. We find that Cooper-pair tunneling in such chainsis completely suppressed. Instead, charge transport is dominated by tunnelingof single electrons, which is very sensitive to the presence of BCSquasiparticles on the superconducting islands of the chain. Consequently weobserve a strong parity effect, where the threshold voltage vanishes sharply ata characteristic parity temperature $T^*$, which is significantly lower thanthe the critical temperature, $T_c$. A measurable and thermally-activatedzero-bias conductance appears above $T^*$, with an activation energy equal tothe superconducting gap, confirming the role of thermally-excitedquasiparticles. Conduction below $T^*$ and above the voltage threshold occursvia injection of single electrons/holes into the Cooper-pair insulator, forminga non-equilibrium steady state with a significantly enhanced effectivetemperature. Our results explicitly show that single-electron transportdominates deep in the insulating state of Josephson-junction arrays. Thisconduction process has mostly been ignored in previous studies of bothsuperconducting junction arrays and granular superconducting films below thesuperconductor-insulator quantum phase transition.

Parity effect and single-electron injection for Josephson-junction chains deep in the insulating state