Commensurability Pinning versus Impurity Pinning of One-Dimensional Charge Density Wave

Abstract

Competition between the commensurability pinning and the impurity pinning on the existence of the long range order is examined at absolute zero in the case of the weak impurity pinning of the one-dimensional charge density wave. There exists a critical value of the commensurability energy, l 0 / d =1.4, which separates the state with long range order (charge density wave (CDW) state) and that without it (charge density glass (CDG) state). Here l 0 and d are the domain size in the absence of commensurability energy and the size of a soliton in the absence of the impurity potential respectively. It is argued that near the boundary of the CDW state and CDG state the average of the formation energy of a localized excitation (a soliton) is decreased whereas that of a extended excitation (a phason) remain essentially unchanged.