Critical and Qualitative Behavior of Sliding Charge Density Waves

This thesis examines, using numerical and analytical methods, the behavior of models for sliding charge density waves. The standard classical model of a charge density wave (CDW) as an elastic medium subject to drive and pinning forces has been very successful in explaining many experimental results for materials that undergo a CDW transition. This simple model accounts for the observed hysteretic behavior and the existence of an electric-field driven depinning transition between the static and sliding CDW states. The richness of this model is due to its essential many-degree -of-freedom character. The qualitative behavior of CDW models is examined. Various bounds on the behavior are demonstrated and the CDW current is shown to be a non-hysteretic function of applied field. It is shown that the solution to the equations of motion is unique in the sliding state. Variations on the standard model are discussed, and a new model is introduced. The critical behavior is examined numerically as the depinning transition is approached from the static and sliding states. The behavior in the static state is history dependent; two distinct approaches to threshold in the static state exhibit scaling behavior that is dissimilar in many respects. There is evidence, however, for a common frequency scale. Finite-size effects indicate the existence of two diverging length scales. The behavior of the CDW velocity in the sliding state also exhibits scaling behavior near the depinning transition. Surprisingly, two models which have distinct mean-field behaviors are found to have consistent scaling behavior in finite-range models, suggesting a broad universality for the critical behavior. Numerical values for the critical exponent for the velocity are in disagreement with previous results; it is claimed that these simulations are the first to explore the critical regime. As in the static state, there are two length scales which diverge as threshold is approached; the resulting double crossover seen in finite samples is qualitatively similar to the finite-size effects in mean field theory, which are studied in an appendix.