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

Abstract

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 Tc DC superconducting quantum interference devices (SQUIDs) in restricted conditions.