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

It has long been thought that superconductivity breaks down in one dimension due to enhanced quantum phase fluctuations. However, the exact mechanism for this is still an active research area. One common feature of existing theories is the idea of ``quantum phase-slip'' (QPS): quantum tunneling of the superconducting order parameter between states where the relative phase between the wire ends differs by $\pm 2\pi$. Many experiments have been carried out to investigate QPS, and a wide range of phenomena have been observed, including resistive fluctuations well below $T_C$ and an apparent quantum phase transition to an insulating state in the narrowest wires. Although these are all likely connected to QPS, a unified understanding has not yet been possible. I will describe a theory for QPS which is based on the idea that flux-charge duality, a classical symmetry of Maxwell's equations, relates the phase fluctuations associated with QPS to the well-known charge fluctuations associated with Josephson tunneling, at a microscopic level. The predictions of this theory compare favorably with a wide range of experimental observations, and may also provide a conceptual link to 2D phase fluctuation phenomena and insulating transitions in thin films.