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Dispersion interaction between crossed conducting wires

J. Dobson,T. Gould,I. Klich

Published 2009 in Physical Review A

ABSTRACT

We compute the T = 0K Van der Waals (nonretarded Casimir) interaction energy E between two inflnitely long, crossed conducting wires separated by a minimum distance D much greater than their radius. We flnd that, up to a logarithmic correction factor, E / iD i1 jsinµj i1 f(µ) where f(µ) is a smooth bounded function of the angle µ between the wires. We recover a conventional result of the form E / iD i4 jsinµj i 1 g(µ) when we include an electronic energy gap in our calculation. Our prediction of gap-dependent energetics may be observable experimentally for carbon nanotubes, either via AFM detection of the vdW force or torque, or indirectly via observation of mechanical oscillations. This shows that strictly parallel wires, as assumed in previous predictions, are not needed to see a novel efiect of this type. At the micro- and nano-scale, dispersion (van der Waals, vdW) forces are ubiquitous [1], and recent advances in manufacturing and measurement techniques have prompted much interest in their precise form. The simplest theories sum vdW interaction energies between pairs of molecules, which is a good approximation for dilute insulating objects, where the dipole ∞uctuations at difierent points of one body are almost independent. For non-dilute dielectric and magnetic materials this summation approximation can be misleading, and may even give the wrong sign of the interaction [2]. Moreover, for anisotropic conducting nanostructures, the non-locality of Coulomb screening and associated density correlations within each object may change the form of the dispersive forces altogether [3, 4]. This physics is exemplifled by the class of quasi-1D objects, which exhibit correlation phenomena of both theoretical and experimental interest. Indeed, in the extreme limit truly conflned 1D electrons experience a Luttinger liquid instability, as (e.g.) in single walled armchair nanotubes [5]. When two such "wires" are placed parallel and close to each other, the coulomb interaction between their density ∞uctuations may become a relevant perturbation, resulting in rich behavior at low temperatures and densities, such as locked charge density waves and Wigner cristallization. [6]. The density density interaction is also responsible for coulomb drag phenomena whereby a current applied to one wire induces voltage on the other wire [7, 8].

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