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We analyze the crossover from an hc/e-periodicity of the persistent currentin flux threaded clean metallic rings towards an hc/2e-flux periodicity of thesupercurrent upon entering the superconducting state. On the basis of a modelcalculation for a one-dimensional ring we identify the underlying mechanism,which balances the hc/e versus the hc/2e periodic components of the currentdensity. When the ring circumference exceeds the coherence length of thesuperconductor, the flux dependence is strictly hc/2e periodic. Further, wedevelop a multi-channel model which reduces the Bogoliubov - de Gennesequations to a one-dimensional differential equation for the radial componentof the wave function. The discretization of this differential equationintroduces transverse channels, whose number scales with the thickness of thering. The periodicity crossover is analyzed close the critical temperature.

Crossover from hc/e to hc/2e current oscillations in rings of s-wave superconductors