Perturbation theory of superconducting micronetworks near the phase-transition boundary

A perturbation theory for micronetworks is developed which is valid near the second-order phase boundary. Perturbation equations to general order in terms of the nodal order parameter are derived. Explicit corrections to first order in temperature T and magnetic flux φ are obtained from the latter equations. This scheme is then applied to the infinite ladder. Stability limits in terms of the Gibbs free energy are derived for different spatial vortex solutions. Furthermore, the shielding currents of the ladder for ‖φ‖<0.21${\phi }_0$ are calculated (${\phi }_0$ is the fluxoid quantum) near the phase boundary as a function of ΔT and Δφ and are compared to our numerical solutions of the nonlinear Ginzburg-Landau equations. The agreement is very good. Similarly, very good agreement is obtained for the order parameter near φ=0.5${\phi }_0$. Expressions for magnetization, differential susceptibility, entropy difference, and specific-heat jump near the phase-transition boundary of the ladder are derived.