Vortex blockade and conductance fluctuations of superconducting strips in magnetic fields

Recent experiments on the conductance of a thin, narrow superconducting strip found periodic fluctuations as a function of the perpendicular magnetic field, with the period corresponding to approximately two flux quanta per strip area [1]. Using vortex-charge duality, we explore the possibility that the superconducting strip is the dual of a quantum dot, with vortices playing the role of the electrons, the magnetic field appearing as the gate voltage, and the applied current replacing the source-drain voltage. As with a quantum dot, extrema of the conductance are obtained when configurations with $n$ and $n+1$ vortices have equal energy; in the bias-current versus magnetic-field plane, the conductance displays blockade diamonds. Furthermore, we find that there is a simple relation between the linear-response conductance and the critical current, as they are both set by the barrier to vortex tunneling on to and off of the strip. [1] A. Johansson et al. Phys. Rev. Lett. 95, 116805 (2005).