Simple model for plastic dynamics of a disordered flux-line lattice

Abstract

We use a coarse-grained model of superconducting vortices driven through a random pinning potential to study the nonlinear current-voltage (IV) characteristics of flux flow in type II superconductors with pinning. In experiments, the IV relation measures flux flow down a flux density gradient. The work presented here treats this key feature explicitly. As the vortex repulsion weakens, the vortex pile maintains a globally steeper slope, corresponding to a larger critical current, for the same pinning potential. In addition, the magnitude of the peak in the differential resistance falls as the resistance peak shifts to higher currents. The model also exhibits so-called "IV fingerprints", and crossover to Ohmic (linear) behavior at high currents. Thus, many of the varieties of plastic behavior observed experimentally for soft flux line systems in the "peak regime" are reproduced in numerical simulations of the zero temperature model. This model describes a two-dimensional slice of the flux line system at the scale of the London length (λ). It does not include any degrees of freedom at scales much smaller than λ, which are required to specify the degree of disorder in a flux line lattice. Instead, the nonlinear transport behaviors are related to the self-organized, large scale morphologies of the vortex river flow down the slope of the vortex pile. These morphologies include isolated filamentary channels, which can merge at higher flow rates to make a braided river, and eventually give uniform flow at even higher flow rates. The filamentary structure is associated with an IV characteristic that has concave, or positive, curvature. The braided river is associated with the peak in the differential resistance, where the curvature of the IV relation changes to convex. The transition to Ohmic behavior comes about as the braided river floods when it cannot absorb a higher level of flow. We propose that these self-organized morphologies of flux flow down a flux gradient govern the various plastic flow behaviors, including nonlinear IV characteristics, observed in type II superconductors with random pinning.

Irreversible flow of vortex matter: Polycrystal and amorphous phases

“…[34][35][36][37][38] Depending on simulation parameters, it is found to proceed either in individual well-defined channels or in several weakly coupled rivers. Such observations have also inspired a recent field theoretical formulation of the plastic depinning problem, which is supposed to provide a reliable picture of irreversible transport whenever layered dynamics occur.…”

Dynamic transition in current-driven disordered flux-line lattice in single-crystal of Bi-2212

“…In the plastic flow regime, depinning is observed to occur through plastic channels between pinned regions [12]. This type of plastic flow is observed in experiments [17] numerical simulations studies [18,19] …”

Filamentary flow of vortices in aBi2Sr2Ca1Cu2O8<

“…Here, the observed vortex dynamics confirms that the vortex flow morphologically changes from filamentary strings to a braided river as 0 H is increased, which has been proposed in recent numerical simulations results of superconducting vortices driven by repulsive interactions through a random pinning potential. 43,44 This plastic flow regime is also accompanied by a pronounced fingerprint effect. The jaggedness or fingerprints are generally attributed to the opening and the closing of channels as the applied current increases.…”