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

We use a coarse-grained model of superconducting vortices driven through a random pinning potential to study the nonlinear current-voltage (I-V) characteristics of flux flow in type-II superconductors with pinning. In experiments, the I-V relation measures flux now 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 "I-V fingerprints" and crossover to Ohmic (linear) behavior at high currents. Thus. many of the experimentally observed characteristics associated with the plastic flow of soft flux-line systems 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 (lambda). It does not include any degrees of freedom at scales much smaller than lambda, 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 I-V characteristic that has concave. or positive, curvature. The braided river is associated with the peak in the differential resistance, where the curvature of the I-V 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 I-V characteristics, observed in type-II superconductors with random pinning.