Superconducting insulators and localization of Cooper pairs

Rapid miniaturization of electronic devices and circuits demands profound understanding fluctuation phenomena at the nanoscale. Superconducting nanowires -- serving as important building blocks for such may seriously suffer from fluctuations which tend to destroy long-range order suppress superconductivity. In particular, quantum phase slips (QPS) proliferating low temperatures turn a quasi-one-dimensional superconductor into resistor or an insulator. Here, we introduce physical concept QPS-controlled localization Cooper pairs that occur even in uniform without any dielectric barriers being fundamental manifestation flux-charge duality superconductors. We demonstrate both experimentally theoretically deep "insulating" state actually exhibit non-trivial superposition superconductivity weak Coulomb blockade generated by tunneling magnetic fluxons across wire.