A 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 (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. 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, braided rivers, and flooded rivers. 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.