We have measured the critical current as a function of magnetic field in short and narrow superconducting aluminum nanowires. In the range of magnetic fields in which vortices can enter a nanowire in a single row, we find regular oscillations of the critical current as a function of magnetic field. The oscillations are found to correspond to adding a single vortex to the nanowire, with the number of vortices on the nanowire staying constant within each period of the oscillation. This effect can be thought of as a Weber blockade, and the nanowires act as quantum dots for vortices, analogous to the Coulomb blockade for electrons in quantum dots.
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