Lifshitz-type formulas for graphene and single-wall carbon nanotubes: van der Waals and Casimir interations

TL;DR

This paper derives Lifshitz-type formulas for van der Waals and Casimir interactions involving graphene and carbon nanotubes, providing a theoretical framework for understanding their electromagnetic interactions with various materials and molecules.

Contribution

It introduces new Lifshitz-type formulas for graphene and nanotubes based on boundary conditions of a charged plasma sheet, extending the theoretical understanding of their electromagnetic interactions.

Findings

Formulas applied to graphene-Au and Si interactions.

Results for hydrogen atoms and molecules with graphene.

Interaction analysis for single-wall carbon nanotubes with substrates.

Abstract

Lifshitz-type formulas are obtained for the van der Waals and Casimir interaction between graphene and a material plate, graphene and an atom or a molecule, and between a single-wall carbon nanotube and a plate. The reflection properties of electromagnetic oscillations on graphene are governed by the specific boundary conditions imposed on the infinitely thin positively charged plasma sheet, carrying a continuous fluid with some mass and charge density. The obtained formulas are applied to graphene interacting with Au and Si plates, to hydrogen atoms and molecules interacting with graphene, and to single-wall carbon nanotubes interacting with Au and Si plates. The generalizations to more complicated carbon nanostructures are discussed.