A Fast Semi-Implicit Finite-Difference Method for the TDGL Equations

With increasing applied current we show that the moving vortex lattice changes its structure from a triangular one to a set of parallel vortex rows in a pinning free superconductor. This effect originates from the change of the shape of the vortex core due to non-equilibrium effects (similar to the mechanism of vortex motion instability in the Larkin-Ovchinnikov theory). The moving vortex creates a deficit of quasiparticles in front of its motion and an excess of quasiparticles behind the core of the moving vortex. This results in the appearance of a wake (region with suppressed order parameter) behind the vortex which attracts other vortices resulting in an effective direction-dependent interaction between vortices. When the vortex velocity v reaches the critical value vc quasi-phase slip lines (lines with fast vortex motion) appear which may coexist with slowly moving vortices between such lines. Our results are found within the framework of the timedependent Ginzburg-Landau equations and are strictly valid when the coherence length ξ(T ) is larger or comparable with the decay length Lin of the non-equilibrium quasiparticle distribution function. We qualitatively explain experiments on the instability of vortex flow at low magnetic fields when the distance between vortices a ≫ Lin ≫ ξ(T ). We speculate that a similar instability of the vortex lattice should exist for v > vc even when a < Lin.

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“…The semi-implicit algorithm was used [28] which provides an effective numerical solution of Eqs. 1(a,b) for the case of large κ values.…”

Section: Model Systemmentioning

confidence: 99%

Rearrangement of the vortex lattice due to instabilities of vortex flow

2007

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“…In addition, a Crank-Nicolson 1 algorithm established for solving the superfluid GrossPitaevskii equations 2 has been adapted for solving the timedependent Ginzburg-Landau equations, 3 which provides a further improvement in efficiency of one or two orders of magnitude. These improvements permit the use of TDGL computation to model superconductors with high finite values in contact with nonsuperconducting materials.…”

Section: Introductionmentioning

confidence: 99%

Numerical studies on the effect of normal-metal coatings on the magnetization characteristics of type-II superconductors

Carty

Machida²,

Hampshire

2005

Phys. Rev. B

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(2005) 'Numerical studies on the e ect of normal-metal coatings on the magnetization characteristics of type-II superconductors. ', Physical review B., 71 (14). p. 144507.Further information on publisher's website: Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Magnetic properties of superconductors coated with metals of arbitrary resistivity N are calculated using the time-dependent Ginzburg-Landau equations in which both T c and N vary. As N in the coating is reduced, the initial vortex penetration field H p ͑ N ͒ does not decrease monotonically from the insulating ͑Matricon͒ limit to the extreme metallic ͑Bean-Livingston͒ limit, but has a minimum value H p͑min͒ below the extreme metallic value. The minimum occurs because the barrier is weakened by proximity-effect penetration of superelectrons into the coating which only occurs at finite resistivity. In an applied magnetic field, local depressions in nucleate in the coating which do not have the well-known quantum of magnetic flux ͑h /2e͒ until they have crossed the coating and entered the interior of the superconductor. When T = 0 and T c of the normal metal coating is zero, the minimum vortex penetration field H p͑min͒ Ϸ 0.76 −1.17 H c2 which occurs for a coating resistivity N Ϸ 1.1 −0.6 S . For T Ͼ 0 the minimum is attenuated. Adding a thick weakly superconducting SЈ layer between the superconductor and normal metal coating reduces the irreversibility markedly.

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“…In this work, the TDGL equations in the zero electric potential gauge were solved in 2D using the finite difference semiimplicit Crank-Nicolson algorithm developed by Winiecki and Adams [18]. It is based on the widely-used U-method described by Gropp et al [19].…”

Section: Methodsmentioning

confidence: 99%