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

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.

Repulsive vacuum-induced forces on a magnetic particle

“…Particularly, the response of the metal at zero frequency is largely different between the two models. For example, while the Fresnel coefficient r s (κ ⊥ , 0) → 0 for the Drude model, it is non-vanishing for the plasma model [74]. As we have seen from Eq.…”

“…The key difference in the two models is that the plasma model disregards the relaxation of conducting electrons in the metal. This difference matters the most for the low frequency response of the metals, and can lead to very different resulting Casimir forces [72][73][74]. Such a discrepancy has been much debated in the literature, with the experimental results favoring the plasma model in some cases, and Drude in others [75][76][77][78][79][80][81].…”

Quantum thermodynamics of overdamped modes in local and spatially dispersive materials

“…It is prohibited, however, once certain statistical properties (in our case the Pauli exclusion principle via the Fermi-Dirac statistics) enter the description of the system. Finally, we would like to note that the above description can also account for certain properties of the Casimir free energy in metallic films [126]. Here, it was shown that in the limit of a diverging plasma frequency, for which the perfect electric conductor limit should be recovered, the Drude model and its non-dissipative version, the plasma model, behave quite differently.…”

Casimir forces in the flatland: Interplay between photoinduced phase transitions and quantum Hall physics

“…Having a finite dissipation, even if arbitrarily small, is fundamentally different from having no dissipation. For metallic materials, this is equivalent to describe the system using a plasma (Γ = 0) or a Drude (Γ = 0) model, which leads to significantly different final results [51]. In principle, the Drude model is the most straightforward approach for taking into account the relaxation properties of conduction electrons, and should be applicable in the quasistatic limit (which corresponds to the high temperature regime of the Casimir force).…”