The thermal Casimir effect for rough metallic plates

TL;DR

This paper introduces a new phenomenological model for the thermal Casimir effect between rough metallic surfaces, emphasizing the impact of surface roughness on thermal corrections and aligning with recent experimental data.

Contribution

The paper presents a novel theoretical approach that accounts for surface roughness effects on the thermal Casimir force, especially for metallic surfaces with roughness smaller than the skin depth.

Findings

Surface roughness significantly affects thermal Casimir force corrections.

The model aligns with recent precise measurements of the Casimir force.

Predicts a new thermal correction at larger plate separations.

Abstract

We propose a new theory of thermal Casimir effect, holding for the experimentally important case of metallic surfaces with a roughness having a spatial scale smaller than the skin depth. The theory is based on a simple phenomenological model for a rough conductor, that explicitly takes account of the fact that ohmic conduction in the immediate vicinity of the surface of a conductor is much impeded by surface roughness, if the amplitude of roughness is smaller than the skin depth. As a result of the new model, we find that surface roughness strongly influences the magnitude of the thermal correction to the Casimir force, independently of the plates separation. Our model, while consistent with recent accurate measurements of the Casimir force in the submicron range, leads to a new prediction for the not yet observed thermal correction to the Casimir force at large plates separation. Besides the thermal Casimir problem, our model is relevant for the correct theoretical interpretation of current experiments probing other proximity effects between conductors, like radiative heat transfer and quantum friction.