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It has long been thought that macroscopic phase coherence breaks down ineffectively lower-dimensional superconducting systems even at zero temperaturedue to enhanced topological quantum phase fluctuations. In quasi-1D wires,these fluctuations are described in terms of "quantum phase-slip" (QPS):tunneling of the superconducting order parameter for the wire between statesdiffering by $\pm2\pi$ in their relative phase between the wire's ends. Overthe last several decades, many deviations from conventional bulksuperconducting behavior have been observed in ultra-narrow superconductingnanowires, some of which have been identified with QPS. While at least some ofthe observations are consistent with existing theories for QPS, otherobservations in many cases point to contradictory conclusions or cannot beexplained by these theories. Hence, a unified understanding of the nature ofQPS, and its relationship to the various observations has yet to be achieved.In this paper we present a new model for QPS which takes as its starting pointan idea originally postulated by Mooij and Nazarov [Nature Physics {\bf 2}, 169(2006)]: that \textit{flux-charge duality}, a classical symmetry of Maxwell'sequations, can be used to relate QPS to the well-known Josephson tunneling ofCooper pairs. Our model provides an alternative, and qualitatively different,conceptual basis for QPS and the phenomena which arise from it in experiments,and it appears to permit for the first time a unified understanding ofobservations across several different types of experiments and materialssystems.

Flux-charge duality and topological quantum phase fluctuations in quasi-one-dimensional superconductors