An approach to superconductive micronetworks is presented that makes use of the currents in the loops and the order parameter along branches as fundamental variables. Fluxoid quantization is introduced as a constraint and inductive effects are explicitly taken into account. The theory is made the starting point of a variational formulation which can use any physically sound guess for the order parameter as a trial function to minimize the free energy. For second-order transitions the zeroth-order approximation of de Gennes and Alexander can be used as a trial function. The formalism allows for the amplitude of the order parameter to be determined as a function of temperature and field. A different choice of ansatz allows the theory to describe transitions taking place when external currents are fed. In this paper we apply the new method to some systems, including a superconducting interferometer without Josephson junctions. The results compare quite well with experiments as well as with exact numerical calculations, giving a fair description of these systems.

• Received 27 March 1995

DOI:https://doi.org/10.1103/PhysRevB.52.7495