Casimir force between sharp-shaped conductors

TL;DR

This paper develops a novel electromagnetic scattering approach to accurately compute Casimir forces between sharp-shaped conductors like wedges and cones, crucial for MEM device design and scanning probe applications.

Contribution

It introduces analytical and systematic methods for calculating Casimir interactions involving sharp geometries, extending beyond existing approximations.

Findings

Analytical expressions for wedge-plate Casimir interaction.

Direct application to forces on scanning tunneling probe tips.

Discovery of large temperature dependence in cone-plate interactions.

Abstract

Casimir forces between conductors at the sub-micron scale cannot be ignored in the design and operation of micro-electromechanical (MEM) devices. However, these forces depend non-trivially on geometry, and existing formulae and approximations cannot deal with realistic micro-machinery components with sharp edges and tips. Here, we employ a novel approach to electromagnetic scattering, appropriate to perfect conductors with sharp edges and tips, specifically to wedges and cones. The interaction of these objects with a metal plate (and among themselves) is then computed systematically by a multiple-scattering series. For the wedge, we obtain analytical expressions for the interaction with a plate, as functions of opening angle and tilt, which should provide a particularly useful tool for the design of MEMs. Our result for the Casimir interactions between conducting cones and plates applies directly to the force on the tip of a scanning tunneling probe; the unexpectedly large temperature dependence of the force in these configurations should attract immediate experimental interest.