Electrostatic attraction of coupled Wigner crystals: Finite temperature effects - art. no. 051604

In this paper we present a unified physical picture for the electrostatic a ttraction between two coupled planar Wigner crystals at finite temperature. This model may facilitate our conceptual understanding of counterion-media ted attractions between (highly) similarly charged planes. By adopting an e lastic 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. I n particular, we analyze the temperature dependence of the short-ranged att raction, arising from ground-state configuration, and we argue that thermal fluctuations may drastically reduce its strength. Also, the long-range for ce agrees exactly with that based on the charge-fluctuation approach. Furth ermore, we take quantum contributions to the long-ranged (fluctuation-induc ed) attraction into account and show how the fractional power law, which sc ales as d(-7/2) for large interplanar distance d at zero temperature, cross es over to the classical regime d(-3) via an intermediate regime of d(-2).