Fate of the Josephson effect in thin-film superconductors

The dc Josephson effect refers to the dissipationless electrical current – the supercurrent – that can be sustained across a weak link connecting two bulk superconductors.1 This effect is a probe of the fundamental nature of the superconducting state, which depends crucially on the spatial dimensionality of the superconducting electrodes. For bulk (i.e. threedimensional) superconductors, the superconductivity is most robust, and the Josephson effect is sustained even at nonzero temperature. However, in wires and thin-films (i.e. lowerdimensional superconductors), thermal and quantum fluctuations play a crucial role. In superconducting wires, these effects qualitatively modify the electrical transport across a weak link.2 Despite a number of recent experiments involving weak links between thin-film superconductors,3–6 little theoretical attention has been paid to the nature of the electrical conduction in such systems. Here, we analyze the case of two superconducting thin films connected by a point contact. Remarkably, the Josephson effect is absent at nonzero temperature, and the resistance across the contact is nonzero. Moreover, the point contact re-