Interaction of a phase soliton with charged impurities in a commensurate charge-density-wave system

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Abstract
A model of a DC- or AC-driven underdamped or overdamped commensurate CDW system with randomly distributed charged impurities, and a similar model of a driven damped or overdamped randomly inhomogeneous long Josephson junction are considered. The models are based on an underdamped or overdamped sine-Gordon equation including a driving term and a perturbation that describes a random lattice of local impurities. The lattice may be both sparse and dense, the latter being approximated by continuous random functions. A fundamental assumption is that initially the system contains frozen solitons (kinks) trapped by a disordered potential generated by the random lattice. With increase in the DC drive, the kinks are gradually released. The corresponding current-voltage characteristics (CVCs) are found. In the underdamped version of the model, the CVC proves to be hysteretic, while the overdamped version demonstrates a very pronounced threshold field. In the underdamped model, radiative dissipation is taken into account too. A dependence of AC conductivity on the AC frequency is also found for both models.