Recent experiments on the conductance of thin, narrow superconducting strips have found periodic fluctuations, as a function of the perpendicular magnetic field, with a period corresponding to approximately two flux quanta per strip area [A. Johansson et al., Phys. Rev. Lett. 95, 116805 (2005)]. We argue that the low-energy degrees of freedom responsible for dissipation correspond to vortex motion. Using vortex-charge duality, we show that the superconducting strip behaves as the dual of a quantum dot, with the vortices, magnetic field, and bias current respectively playing the roles of the electrons, gate voltage, and source-drain voltage. In the bias-current versus magnetic-field plane, the strip conductance displays regions of small vortex conductance (i.e., small electrical resistance) that we term "Weber blockade" diamonds, which are dual to Coulomb blockade diamonds in quantum dots.
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Pekker et al. (2011) studied this question.