Casimir-like tunnelling-induced electronic forces

Abstract

We study the quantum forces that act between two nearby conductors due to electronic tunnelling. We derive an expression for these forces by calculating the flux of momentum arising from the overlap of evanescent electronic fields. Our result is written in terms of the electronic reflection amplitudes of the conductors and it has the same structure as Lifshitz's formula for the electromagnetically mediated Casimir forces. We evaluate the tunnelling force between two semiinfinite conductors and between two thin films separated by an insulating gap. We discuss some applications of our results.