Characteristic properties of the Casimir free energy for metal films deposited on metallic plates

TL;DR

This paper compares the Casimir free energy and pressure of thin metal films on metallic plates using different theoretical models, revealing significant discrepancies that can be experimentally tested and have implications for the Casimir puzzle and film stability.

Contribution

It provides a detailed analysis of the Casimir effect for metal films using Lifshitz theory with Drude and plasma models, highlighting differences and experimental discriminability.

Findings

Discrepancies of hundreds to thousands percent between models for films of tens of nanometers.

Casimir free energy can be positive or negative depending on metal combinations.

Sign change of Casimir energy with increasing film thickness for certain metal pairs.

Abstract

The Casimir free energy and pressure of thin metal films deposited on metallic plates are considered using the Lifshitz theory and the Drude and plasma model approaches to the role of conduction electrons. The bound electrons are taken into account by using the complete optical data of film and plate metals. It is shown that for films of several tens of nanometers thickness the Casimir free energy and pressure calculated using these approaches differ by hundreds and thousands percent and can be easily discriminated experimentally. According to our results, the free energy of a metal film does not vanish in the limiting case of ideal metal if the Drude model approach is used in contradiction with the fact that the fluctuating field cannot penetrate in its interior. Numerical computations of the Casimir free energy and pressure of Ag and Au films deposited on Cu and Al plates have been performed using both theoretical approaches. It is shown that the free energy of a film can be both negative and positive depending on the metals used. For a Au film on a Ag plate and vice versa the Casimir energy of a film changes its sign with increasing film thickness. Applications of the obtained results for resolving the Casimir puzzle and the problem of stability of thin films are discussed.