Dispersion interaction between crossed conducting wires

TL;DR

This paper calculates the van der Waals interaction energy between crossed conducting wires, revealing a dependence on the angle and separation that could be experimentally observed in carbon nanotubes, highlighting effects beyond parallel configurations.

Contribution

It provides a new analytical expression for the interaction energy between crossed wires, including the effects of an electronic energy gap, extending previous parallel wire models.

Findings

Interaction energy scales as -D^{-1} with angle dependence

Including an electronic gap changes the scaling to -D^{-4}

Predictions are experimentally testable with carbon nanotubes

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.