Fate of the Josephson effect in thin-film superconductors

The d.c. Josephson effect refers to the dissipationless electrical current—the supercurrent—that can be sustained across a weak link connecting two bulk superconductors. This effect probes the nature of the superconducting state, which depends crucially on spatial dimensionality. For bulk (that is, three-dimensional) superconductors, the superconductivity is most robust and the Josephson effect is sustained even at non-zero temperature. However, in wires and thin films, thermal and quantum fluctuations play a crucial role. In superconducting wires, these effects qualitatively modify the electrical transport across a weak link. Despite several experiments involving weak links between thin-film superconductors, little theoretical attention has been paid to the electrical conduction in such systems. Here, we analyse the case of two superconducting thin films connected by a point contact. Remarkably, the Josephson effect is absent at non-zero temperature. The point-contact resistance is non-zero and varies with temperature in a nearly activated fashion, with a universal energy barrier set by the superfluid stiffness characterizing the films. This behaviour reflects the subtle nature of thin-film superconductors and should be observable in future experiments.