Dynamics of resistive state in thin superconducting channels

TL;DR

This paper theoretically investigates how the resistive state dynamics in narrow superconducting channels depend on parameters like length, current, and electric field penetration, revealing critical behaviors and bifurcations.

Contribution

It identifies new critical values of the parameter u affecting current-voltage characteristics and hysteresis, and analyzes the bifurcation transitions in the superconducting channels.

Findings

Changing u affects the appearance of phase slip centers.

Critical u values determine step-like or hysteretic I-V behavior.

Hysteresis can be eliminated by increasing shunt conductivity.

Abstract

We theoretically study how the dynamics of the resistive state in narrow superconducting channels shunted by an external resistor depends on channel's length $L$, the applied current $j$, and parameter $u$ characterizing the penetration depth of the electric field in the nonequilibrium superconductors. We show that changing $u$ dramatically affects both the behaviour of the current-voltage characteristics of the superconducting channels and the dynamics of their order parameter. Previously, it was demonstrated that when $u$ is less than the critical value $u_{c1}$, which does not depend on $L$, the phase slip centers appear simultaneously at different spots of the channel. Herewith, for $u>u_{c1}$ these centres arise consecutively at the same place. In our work we demonstrate that there is another critical value for $u$. Actually, if $u$ does not exceed a certain value $u_{c2}$, which depends on $L$, the current-voltage characteristic exhibits the step-like behaviour. However, for $u>u_{c2}$ it becomes hysteretic. In this case, with increase of $j$ the steady state, which corresponds to the time independent distribution of the order parameter along the channel, losses its stability at switching current value $j_{sw}$, and time periodic oscillations of both the order parameter and electric filed occur in the channel. As $j$ sweeps down, the periodic dynamics ceases at certain retrapping current value $j_r<j_{sw}$. Shunting the channel by a resistor increases the value of $j_r$, while $j_{sw}$ remains unchanged. Thus, for some high enough conductivity of the shunt $j_r$ and $j_{sw}$ eventually coincide, and the hysteretic loop disappears. We reveal dynamical regimes involved in the hysteresis, and discuss the bifurcation transitions between them.