Stationary Properties of Superconducting Interferometers

A generalized superconducting interferometer, comprising a parallel arrangement of (lumped) inductances and series (lumped) Josephson junctions is considered. Such a system can be seen as the building block of a simplified model of a high-T$\text{}_{c}$ superconductor with its haphazard distribution of Josephson weak links on grain boundaries and lattice defects. It is shown that the system properties can be self-consistently derived from a properly defined potential energy function, taking account of the energies of the system, its current source and external magnetic field. In particular, by solving a stationary problem for this function relative to conditions of constant current bias and constant magnetic flux applied to the system, the critical current of the interferometer can be determined in function of the applied flux. Stationary phase relations and their impact on other system variables are discussed in detail. The theory is applied to the simplest possible system exhibiting all discussed properties, i.e. an interferometer composed of two junctions in series and one junction in parallel.