Flux periodicity in superconducting rings: Comparison to loops with Josephson junctions.

Abstract

Two systems are described, a bare superconducting ring and a ring with an arm whose oscillatory behavior of circulating current and internal magnetic flux as a function of applied magnetic flux is remarkably similar to that of a ring with a weak link or Josephson junction. Exact closed-form solutions of the nonlinear Ginzburg-Landau equations have been found for bare rings with wire diameter 2a(t) and radius R\ensuremath{\lesssim}\ensuremath{\xi}(t). The circulating current and internal flux dependence on the applied flux which follow from the nonlinear solutions show both nonhysteretic and hysteretic regimes depending on the size of the ring. Numerical results for the case of the ring with an arm show that for small ring sizes the critical current varies as ${R}^{\mathrm{\ensuremath{-}}1/2}$ and that the node with a dangling arm (without a current) acts like a ``strong link'' which prevents transitions to the normal state for certain flux ranges. The results show that the periodic behavior of circulating current and internal flux in ring structures is an intrinsic quantum-mechanical feature which is not subordinate to the presence of a weak link, and thus suggests that thin wires in actual networks may supplant Josephson junctions in some instances.