Special features of the thermal Casimir effect across a uniaxial anisotropic film

TL;DR

This paper studies the thermal Casimir effect across a uniaxial anisotropic film, revealing significant retardation effects at nanometer scales and deriving analytic expressions for large film thicknesses, with implications for material design.

Contribution

It provides the first detailed analysis of the thermal Casimir force involving uniaxial anisotropic films, including numerical and analytic results that highlight deviations from nonrelativistic theories.

Findings

Retardation effects are significant even at nanometer scales.

Classical Casimir free energy depends on static dielectric permittivities.

Classical limit occurs at shorter separations than in vacuum cases.

Abstract

We investigate the thermal Casimir force between two parallel plates made of different isotropic materials which are separated by a uniaxial anisotropic film. Numerical computations of the Casimir pressure at T=300K are performed using the complete Lifshitz formula adapted for an anisotropic intervening layer and in the nonrelativistic limit. It is shown that the standard (nonrelativistic) theory of the van der Waals force is not applicable in this case, because the effects of retardation contribute significantly even for film thicknesses of a few nanometers. We have also obtained simple analytic expressions for the classical Casimir free energy and pressure for large film thicknesses (high temperatures). Unlike the case of isotropic intervening films, for two metallic plates the classical Casimir free energy and pressure are shown to depend on the static dielectric permittivities of an anisotropic film. One further interesting feature is that the classical limit is achieved at much shorter separations between the plates than for a vacuum gap. Possible applications of the obtained results are discussed.