Nucleation and growth of the superconducting phase in the presence of a current

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→Jc, the critical depairing 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→Jc, contrary to previous claims.

Source-reported materials — not catalogue approval

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