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 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 → Jc, contrary to previous claims.

Current-carrying states in Fulde-Ferrell-Larkin-Ovchinnikov superconductors

“…22,23 Superconducting state can possibly develop through the formation of a superconducting fluctuation of a finite magnitude (the critical nucleus) below a certain threshold current, similarly to the non-FFLO case. [25][26][27] IV. CONCLUSIONS…”

Numerical effects in the simulation of Ginzburg–Landau models for superconductivity

“…From the microscopic description given in Reference [12] and for slowly varying applied fields, the time-dependent GL equations provide a useful mathematical model, and can be expressed in the form [23][24][25] …”

“…with H c = H c2 /( √ 2 ) and the other details given in References [24,27,28]. For the problems considered here, a gauge is specified such that the scalar potential = 0 in the superconductor bulk domain and the term A ·n = 0 in the boundary condition on * [29,30].…”

Existence of Superconducting Solutions for a Reduced Ginzburg--Landau Model in the Presence of Strong Electric Currents

“…Note that (8) is invariant with respect to the transformation χ → χ + C for any constant C. We set (χ) Ω = 0 in order to eliminate this degree of freedom throughout the paper. The systems (2), (7), and (8) have attracted significant interest among both physicists and mathematicians with [4]- [13] addressing a variety of related problems in a onedimensional setting for a variety boundary conditions and [14] that considers the linearized version of (2) in higher dimensions. A different simplification of (1) was derived in [15] for the same limit κ → ∞ under an additional assumption that J and σ are of order O(κ 2 ) (cf.…”