Effects of Impurities on the Ordered Phases of One-Dimensional Systems
It has long been known that disorder or the presence of impurities cause localization of the single-electron states in one-dimensional systems (1). In addition to this we shall show that such impurities, in general, can have a large effect upon the degree of order which tends to appear as T→O and upon the mean field transition temperature T of any such ordered phases. However, this effect is selective and depending upon the nature of the scattering introduced by the impurities can severely suppress one type of order while leaving another virtually unaffected. The result which we obtain is a generalization to all types of order in one-dimensional systems, of the Anderson-Maki theorem(2,3) on the insensitivity of the singlet superconducting transition temperature to the presence of non-magnetic impurities, while showing a marked depression of Tc with increasing number of mangetic impurities. We show that to each type of ordered state in one dimension, whether it be a charge density wave (CDW), spin density wave (SDW), triplet superconductivity (TS) or singlet superconductivity (SS) there exists a type of impurity scattering mechanism which has a negligible effect upon the mean field transition temperature of this state.
KeywordsCharge Density Wave Interchain Coupling Quasi Classical Limit Charge Density Wave State Triplet Superconductivity
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