Casimir free energy of metallic films: Discriminating between Drude and plasma model approaches

TL;DR

This study compares the Casimir free energy of metallic films calculated using Drude and plasma models, revealing significant differences that can be experimentally distinguished, especially for films around 100 nm thick.

Contribution

It demonstrates that the Drude and plasma models yield markedly different Casimir energies for metallic films, providing a way to experimentally discriminate between these theoretical approaches.

Findings

Drude model predicts a classical limit at ~100 nm thickness.

Plasma model approach does not reach a classical limit, with energy decreasing exponentially.

In the plasma model, free energy approaches zero as plasma frequency increases.

Abstract

We investigate the Casimir free energy of a metallic film either sandwiched between two dielectric plates or in vacuum. It is shown that even for a thin film of several tens of nanometer thickness the Casimir free energy and pressure calculated with the Lifshitz theory using the Drude model and the plasma model approaches take significantly different values and can be easily discriminated. According to our results, the classical limit is already achieved for films of about 100\,nm thickness if the Drude model approach is used in calculations. In this case the classical expressions for the Casimir free energy and pressure are common for both configurations considered. If the plasma model approach is used, the classical limit is not achieved for any film thickness. Instead, the Casimir free energy and pressure are decreasing exponentially to zero. When the plasma frequency goes to infinity, the Casimir free energy obtained using the Drude model approach goes to a nonzero limit in contradiction with expectations. If the plasma model approach is used the free energy of metallic film goes to zero in the limit of infinitely large plasma frequency. All analytic results are accompanied by numerical computations performed for a Au film and sapphire plates. The possibilities to observe the predicted effects discriminating between the Drude and plasma model approaches are discussed.