Dispersion interaction between crossed conducting wires

Abstract

We compute the $T=0K$ Van der Waals (nonretarded Casimir) interaction energy $E$ between two infinitely long, crossed conducting wires separated by a minimum distance $D$ much greater than their radius. We find that, up to a logarithmic correction factor, $E\propto -D^{-1}|\sin \theta {|}^{-1}f(\theta )$ where $f(\theta )$ is a smooth bounded function of the angle $\theta$ between the wires. We recover a conventional result of the form $E\propto -D^{-4}|\sin \theta {|}^{-1}g(\theta )$ 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 effect of this type.

4 pp, 1 fig, 1 table

References in corpus (5)

• Casimir forces between cylinders and plates
• Casimir manipulations: The orientation dependence of fluctuation-induced forces
• van der Waals Interactions Between Thin Metallic Wires and Layers
• van der Waals dispersion power laws for cleavage, exfoliation and stretching in multi-scale, layered systems
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