Anomalous D.C. Current Singularities Due to Fluxon Motion with Ohmic Dissipation in Josephson Transmission Line

Abstract

The current-voltage (I-V) characteristics due to the fluxon propagation in the Josephson transmission line is calculated, assuming the Ohmic resistance for tunneling quasiparticles as the dominant energy dissipation mechanism of flux on motion. The result yields a comparable order of magnitude of the anomalous d.c. current branches to the ones, observed in the ex­ periment. The magnitude of the dissipation coefficient is estimated from the experimental data, and it yields the reasonable magnitude of the background linear foot part of the I-V characteristics. Recently the nonlinear wave excitations have been recognized as the essen­ tial entities characterizing the dynamical responses of various systems in solid state physics. I) A remarkable example of such phenomena is the anomalous d.c. current singularities (ADCS )/H) observed in a Josephson junction with length far longer than the Josephson penetration length Aj (to be called Josephson trans­ mission line or JTL hereafter). The ADCS appear in a series of branches in the voltage region e V < 2L1( T) (L1( T); energy gap of the electrode superconductors) of I-V characteristics of JTL where ordinary quasiparticle current is not ex­ pected. The first theoretical interpretation of the phenomenon was proposed by Fulton and Dynes (FD )4) who ascribed the origin of the ADCS to the propagation of vortex lines along the JTL. Treating the vortex line as a rigid particle with flux quantum (fJo and taking account of the effect of weak dissipative forces, FD succeeded in deriving the essential features of the ADCS in the I-V characteristics of JTL. Their idea has been refined in the work by Costabile, Parmentier, Savo, Mclaughlin and Scott,5) who developed a theory of nonlinear wave excitations of sine-Gordon (s-G) equation for the phase difference ¢(x, t) of the order param­ eter of electrode superconductors. In order to take account of the effects due to finite length of JTL, Costabile et al. imposed the open-circuit boundary condition on the solutions of s-G equation and constructed a group of nonlinear wave excitations (called fluxons) which were to be identified with the propagating vortex lines in FD's theory. They calculated the I-V characteristics due to propagation of the fluxons, taking account of the weak dissipation in terms of power balance equation. The calculated characteristics reproduced the main