Kinematic vortices induced by defects in gapless superconductors

The generalized time-dependent Ginzburg-Landau (GTDGL) theory was first proposed to describe better gap superconductors and the phenomenon of thermal phase-slips (PSs) in defect-free systems. However, there is a lack of information about studies involving PSs in mesoscopic superconductors with surface defects. Thus, in this work, we simulated samples with two co-linear surface defects consisting of a lower $T_c$ superconductor narrowing the sample in its central part. The non-linear GTDGL equations were solved self-consistently under variable applied currents and by considering both gapless and gap-like superconductors. In such systems, the currents passing by the constriction induce the appearance of kinematic vortices even in the gapless sample. The dynamics always occur with a pair forming at opposite edges of the sample and annihilating in the center. It is noticed that the resistive state appears at distinct values of the applied current density for different samples, and the critical current presents a tiny difference between gapless and gap-like samples. It is worth mentioning that parameters such as the size of electrical contacts and constriction affect the critical current and the average velocity of the kinematic vortices.