Title: Metastability and bifurcation in superconducting nanorings,
Abstract: We describe an approach, based on direct numerical solution of the Usadel
equation, to finding stationary points of the free energy of superconducting
nanorings. We consider both uniform (equilibrium) solutions and the critical
droplets that mediate activated transitions between them. For the uniform
solutions, we compute the critical current as a function of the temperature,
thus obtaining a correction factor to Bardeen's 1962 interpolation formula. For
the droplets, we present a metastability chart that shows the activation energy
as a function of the temperature and current. A comparison of the activation
energy for a ring to experimental results for a wire connected to
superconducting leads reveals a discrepancy at large currents. We discuss
possible reasons for it. We also discuss the nature of the bifurcation point at
which the droplet merges with the uniform solution.