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

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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.

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  1. 1.

    A. A. Abrikosov and I. A. Ryzhkin,Adv. Phys. 27, 147 (1978).

  2. 2.

    J. T. Devreese, R. P. Evrard, and V. E. van Doren, eds.,Highly Conducting One-Dimensional Solids (Plenum Press, New York, 1979).

  3. 3.

    V. L. Berezinsky and L. P. Gor'kov,Zh. Eksp. Teor. Fiz. 77, 2498 (1979);78, 813 (1980).

  4. 4.

    A. A. Abrikosov,J. Low Temp. Phys. 10, 3 (1973).

  5. 5.

    L. P. Gor'kov and O. N. Dorokhov,Fiz. Nizkikh Temp. 4, 332 (1978).

  6. 6.

    A. A. Abrikosov, L. P. Gor'kov, and I. Ye. Dzyaloshinski,Methods of Quantum Field Theory in Statistical Physics (Prentice Hall, 1963).

  7. 7.

    A. A. Abrikosov,Solid State Comm. 37, 997 (1981).

  8. 8.

    A. A. Ovchinnikov and N. S. Erikhman,Zh. Eksp. Teor. Fiz. 78, 1449 (1980).

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Abrikosov, A.A., Dorotheyev, E.A. The Peierls transition and electron localization by a random potential in a one-dimensional conductor. J Low Temp Phys 46, 53–69 (1982).

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  • Charge Density
  • Critical Temperature
  • Fermi Level
  • State Density
  • Impurity Concentration