Theory of the threshold field for the depinning transition of a charge density wave

Abstract

The Hamiltonian of an elastic string pinned by random potentials is often used to describe the depinning transition of a charge density wave in the presence of impurity pinning. The properties of the pinned states show close analogies to those of glassy systems, while the depinning transition resembles a dynamical critical phenomenon. Here we develop an approximate analytical approach based on the quasi-harmonic treatment of the nonlinear pinning potentials together with an expression of the correlation functions to lowest order. This method allows a nonperturbative treatment of a problem with many nonlinear degrees of freedom and quenched disorder. In this way it is possible to characterize the pinned configurations and to compute the threshold field as a function of the coupling constant of the model. The results are in very good agreement with the computer simulations for strong and intermediate pinning and provide an approximate but quantitative method for the determination of the pinned-unpinned phase diagram.