Supercurrent dephasing by electron-electron interactions
We demonstrate that in sufficiently long diffusive superconducting-normal-superconducting (SNS) junctions dc Josephson current is exponentially suppressed by electron-electron interactions down to zero temperature. This suppression is caused by the effect of Cooper pair dephasing which occurs in the normal metal and defines a new fundamental length scale Lφ in the problem. This length is fully consistent with that derived earlier from the analysis of dissipative electron transport across NS interfaces at subgap energies. Provided the temperature length exceeds Lφ this dephasing length can be conveniently extracted from equilibrium measurements of the Josephson current.