Superconductivity in a mesoscopic double square loop: Effect of imperfections

We have generalized the network approach to include the effects of short-range imperfections in order to analyze recent experiments on mesoscopic superconducting double loops. The presence of weakly scattering imperfections causes gaps in the phase boundary B(T) or Φ(T) for certain intervals of T, which depend on the magnetic flux penetrating each loop. This is accompanied by a critical temperature T_c(Φ), showing a smooth transition between symmetric and antisymmetric states. When the scattering strength of imperfections increases beyond a certain limit, gaps in the phase boundary T_c(B) or T_c(Φ) appear for values of magnetic flux lying in intervals around half-integer Φ₀=hc/2e. The critical temperature corresponding to these values of magnetic flux is determined mainly by imperfections in the central branch. The calculated phase boundary is in good agreement with experiment.