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Electrostatic attraction of coupled Wigner crystals: Finite temperature effects

A. W. C. Lau1,2, P. Pincus2,3, Dov Levine4, and H. A. Fertig5

  • 1Laboratoire de Physique de la Matière Condensée, Collège de France, 11 Place Marcelin Berthelot, 75231 Paris Cedex 05, France
  • 2Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106-9530
  • 3Material Research Laboratory, University of California Santa Barbara, Santa Barbara, California 93106-9530
  • 4Physics Department, Technion–Israel Institute of Technology, Haifa 32000, Israel
  • 5Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506-0055

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Phys. Rev. E 63, 051604 – Published 23 April, 2001

DOI: https://doi.org/10.1103/PhysRevE.63.051604

Abstract

In this paper we present a unified physical picture for the electrostatic attraction between two coupled planar Wigner crystals at finite temperature. This model may facilitate our conceptual understanding of counterion-mediated attractions between (highly) similarly charged planes. By adopting an elastic theory, we show that the total attractive force between them can be (approximately) decomposed into a short-ranged and a long-ranged component. They are evaluated below the melting temperature of the Wigner crystals. In particular, we analyze the temperature dependence of the short-ranged attraction, arising from ground-state configuration, and we argue that thermal fluctuations may drastically reduce its strength. Also, the long-range force agrees exactly with that based on the charge-fluctuation approach. Furthermore, we take quantum contributions to the long-ranged (fluctuation-induced) attraction into account and show how the fractional power law, which scales as d−7/2 for large interplanar distance d at zero temperature, crosses over to the classical regime d−3 via an intermediate regime of d−2.

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Outline

Information

Phys. Rev. E 63, 051604– Published 23 April, 2001
  • Received 16 June 2000

© 2001 American Physical Society

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