Josephson Effect in a Superconducting Ring

Abstract

The Josephson effect in a superconducting ring, interrupted by a barrier, is shown to be the direct consequence of fundamental principles and, hence, to exactly obey the voltage-frequency relation used for a precise determination of $\frac{e}{h}$. Supplementary considerations deal with the role of electron pairing and with additional features such as those found in the presence of two parallel junctions. The special case of a thin ring is used to illustrate the treatment of dynamical properties, including the possible occurrence of hysteresis. A more detailed discussion of the effects due to a potential barrier is presented, followed by a rederivation of Josephson's differential equation which is seen to govern the time dependence of the penetrating flux.