Van Der Waals and Casimir Interactions of Some Graphene, Material Plate and CNTs Systems

The Van der Waals and Casimir interactions between graphene and a material plate are studied by using the Lifshitz theory and approximate expressions for the free energy and force. The reflection properties of electromagnetic oscillations on graphene are governed by 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 the cases of a graphene interacting with Au plate. We calculated also the Casimir interaction between carbon nanotube single wall and Au plate. The comparision with other recently obtained theoretical results are made and the generalizations to more complicated carbon nanostructures are discussed.