Introduction. Quantifying the flux through a superconducting loop

In a superconductor, whose temperature T is below its critical temperature T _c , some of the free electrons associate in pairs, known as Cooper pairs, which obey the Bose-Einstein statistics and therefore tend to occupy the same quantum state. This quantum state is described by a macroscopic wave function.

Consider a ring of superconducting material at a temperature below T _c . At a given position in the ring, the macroscopic wave function representing the superconducting state is monovalent, so the phase of this wave function there is defined modulo 2π. We show that the circulation of this phase along the ring (outline $\mathcal{C}$ on figure