Nucleation and Growth of the Superconducting Phase in the Presence of a Current

TL;DR

This paper investigates the behavior of superconducting phase nucleation under current using Ginzburg-Landau equations, revealing how solutions evolve with current and material parameters through numerical and asymptotic analysis.

Contribution

It provides a detailed numerical and analytical study of stationary solutions and interface dynamics in superconductors under current, including asymptotic behaviors for different parameter regimes.

Findings

Threshold solutions are exponentially small in current.

Interface width diverges as current approaches stall current J*.

Interface velocities are bounded as J approaches 0 and J_c.

Abstract

We study the localized stationary solutions of the one-dimensional time-dependent Ginzburg-Landau equations in the presence of a current. These threshold perturbations separate undercritical perturbations which return to the normal phase from overcritical perturbations which lead to the superconducting phase. Careful numerical work in the small-current limit shows that the amplitude of these solutions is exponentially small in the current; we provide an approximate analysis which captures this behavior. As the current is increased toward the stall current J*, the width of these solutions diverges resulting in widely separated normal-superconducting interfaces. We map out numerically the dependence of J* on u (a parameter characterizing the material) and use asymptotic analysis to derive the behaviors for large u (J* ~ u^-1/4) and small u (J -> J_c, the critical deparing current), which agree with the numerical work in these regimes. For currents other than J* the interface moves, and in this case we study the interface velocity as a function of u and J. We find that the velocities are bounded both as J -> 0 and as J -> J_c, contrary to previous claims.