Analytical results of the Fokker-Planck equation derived for one superconducting nanowire quantum interference device and for DC SQUID: symmetric devices

摘要

We consider a symmetric two- junction superconducting quantum interference device, whose junctions are assumed to be overdamped, and consider the sin Fourier series for their current - phase relations. We take into account the effects of thermal fluctuations by forming a two- dimensional Fokker - Planck equation for the distribution function. We judge a series expansion of first order with respect to the components of the reduced inductance for the distribution function and obtain relations for current - voltage and the circulating current. We consider the measured resistance of the superconducting nanowire quantum interference device with mesoscopic leads that Hopkins et al reported in Hopkins et al ( 2005 Science 308 1762) and Pekker et al ( 2005 Phys. Rev. B 72 104517), by defining the loop inductance, and by considering appropriate relations for the resistance of nanowires. In fact, we extend the Chesca formulation ( Chesca 1998 J. Low Temp. Phys. 112 165) and give a unification formulation for symmetric nanowire two- junction devices, low and high T-c DC superconducting quantum interference devices ( SQUIDs) in restricted conditions.