The Josephson supercurrent-phase relation

Superconducting rings which are interrupted by a weak superconducting junction (SQUID) can attain two different metastable magnetic flux states when they are placed in a magnetic field of appropriate strength. In the preceding article of this issue in Physica B measurements are discussed on the observation of intrinsic magnetic flux transitions due to thermal activation over the potential barrier separating the two states. With respect to the interpretation of our data we investigated the consequences of deviations from the Josephson sinusoidal supercurrent-phase relation for the magnitude of the barrier height. In this article the supercurrent-phase relations are reviewed for different types of weak links, for instance: the well known Josephson oxide junction, narrow superconducting constrictions in the dirty and clean limit for the complete temperature range, etc. Calculations are presented which show the strong consequences for the barrier height: the barrier height increases when compared with a calculation based on a sinusoidal behaviour.