Operation of a superconducting nanowire quantum interference device with   mesoscopic leads
  A theory describing the operation of a superconducting nanowire quantum interference device (NQUID) is presented. The device consists of a pair of thin-film superconducting leads connected by a pair of topologically parallel ultra-narrow superconducting wires. It exhibits intrinsic electrical resistance, due to thermally-activated dissipative fluctuations of the superconducting order parameter. Attention is given to the dependence of this resistance on the strength of an externally applied magnetic field aligned perpendicular to the leads, for lead dimensions such that there is essentially complete and uniform penetration of the leads by the magnetic field. This regime, in which at least one of the lead dimensions lies between the superconducting coherence and penetration lengths, is referred to as the mesoscopic regime. The magnetic field causes a pronounced oscillation of the device resistance, with a period not dominated by the Aharonov-Bohm effect through the area enclosed by the wires and the film edges but, rather, in terms of the geometry of the leads, in contrast to the well-known Little-Parks resistance of thin-walled superconducting cylinders. A theory, encompassing this phenomenology, is developed through extensions, to the setting of parallel superconducting wires, of the Ivanchenko-Zil'berman-Ambegaokar-Halperin theory for the case of short wires and the Langer-Ambegaokar-McCumber-Halperin theory for the case of longer wires. It is demonstrated that the NQUID acts as a probe of spatial variations in the superconducting order parameter. 
David Pekker, Alexey Bezryadin, David S. Hopkins, and Paul M. Goldbart