Journal of Low Temperature Physics

, Volume 46, Issue 1–2, pp 53–69 | Cite as

The Peierls transition and electron localization by a random potential in a one-dimensional conductor

  • A. A. Abrikosov
  • E. A. Dorotheyev


The influence of a random impurity potential on a simple model of a one-dimensional metal undergoing a Peierls transition is considered. The following properties are studied: the order parameter, the transition temperature, the state density. Contrary to the “kinetic” approach, where only nonintersecting impurity lines are taken into account, it appears that the energy gap is absent at any impurity concentration, although at small concentrations the state density at the Fermi level decreases exponentially with concentration. The static conductivity of a finite sample is calculated at various temperatures. The formation of a charge density wave enhances localization: the localization length decreases with increasing order parameter. The conductivity at small but finite frequency is obtained. Close to the critical temperature it decreases rapidly withT c -T.


Charge Density Critical Temperature Fermi Level State Density Impurity Concentration 
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  1. 1.
    A. A. Abrikosov and I. A. Ryzhkin,Adv. Phys. 27, 147 (1978).Google Scholar
  2. 2.
    J. T. Devreese, R. P. Evrard, and V. E. van Doren, eds.,Highly Conducting One-Dimensional Solids (Plenum Press, New York, 1979).Google Scholar
  3. 3.
    V. L. Berezinsky and L. P. Gor'kov,Zh. Eksp. Teor. Fiz. 77, 2498 (1979);78, 813 (1980).Google Scholar
  4. 4.
    A. A. Abrikosov,J. Low Temp. Phys. 10, 3 (1973).Google Scholar
  5. 5.
    L. P. Gor'kov and O. N. Dorokhov,Fiz. Nizkikh Temp. 4, 332 (1978).Google Scholar
  6. 6.
    A. A. Abrikosov, L. P. Gor'kov, and I. Ye. Dzyaloshinski,Methods of Quantum Field Theory in Statistical Physics (Prentice Hall, 1963).Google Scholar
  7. 7.
    A. A. Abrikosov,Solid State Comm. 37, 997 (1981).Google Scholar
  8. 8.
    A. A. Ovchinnikov and N. S. Erikhman,Zh. Eksp. Teor. Fiz. 78, 1449 (1980).Google Scholar

Copyright information

© Plenum Publishing Corporation 1982

Authors and Affiliations

  • A. A. Abrikosov
    • 1
  • E. A. Dorotheyev
    • 1
  1. 1.L.D. Landau Institute for Theoretical PhysicsAcademy of Sciences of USSRMoscowUSSR

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