  Superconductors in a cylindrical geometry respond periodically to a
cylinder-threading magnetic flux, with the period changing from hc/2e to hc/e
depending on whether the Aharonov-Bohm effects are suppressed or not. We show
that Holographic Superconductors present a similar phenomenon, and that the
different periodicities follow from classical no-hair theorems. We also give
the Ginzburg-Landau description of the period-doubling phenomenon.
