Casimir interactions between graphene sheets and metamaterials

The Casimir force between graphene sheets and metamaterials is studied. Theoretical results based on the Lifshitz theory for layered, planar, two-dimensional systems in media are presented. We consider graphene-graphene, graphene-metamaterial, andmetal-graphene-metamaterial configurations. We find that quantum effects of the temperature-dependent force are not apparent until the submicron range. In contrast to results with bulk dielectric and bulk metallic materials, no Casimir repulsion is found when graphene is placed on top of a magnetically active metamaterial substrate, regardless of the strength of the low-frequency magnetic response. In the case of the metal-graphene-metamaterial setting, repulsion between the metamaterial and the metal-graphene system is possible only when the dielectric response from the metal contributes significantly.