Casimir Forces and Graphene Sheets

TL;DR

This paper derives the Casimir force between multiple graphene sheets considering their finite conductivities, revealing that at large distances, the interaction mimics that of perfect conductors but with reduced magnitude due to graphene's unique properties.

Contribution

The study models the Casimir interaction among multiple graphene sheets incorporating their dispersive conductivities, extending previous two-sheet analyses to N sheets.

Findings

Graphene's universal conductivity influences Casimir force magnitude.

At large separations, graphene's Casimir interaction matches perfect conductors' distance dependence.

The interaction magnitude is significantly smaller than that of perfect conductors.

Abstract

The Casimir force between two infinitely thin parallel sheets in a setting of $N$ such sheets is found. The finite two-dimensional conductivities, which describe the dispersive and absorptive properties of each sheet, are taken into account, whereupon the theory is applied to interacting graphenes. By exploring similarities with in-plane optical spectra for graphite, the conductivity of graphene is modeled as a combination of Lorentz type oscillators. We find that the graphene transparency and the existence of a universal constant conductivity $e^2/(4\hbar)$ result in graphene/graphene Casimir interaction at large separations to have the same distance dependence as the one for perfect conductors but with much smaller magnitude.