Many-body effects in van der Waals-Casimir interaction between graphene layers

Van der Waals-Casimir dispersion interactions between two apposed graphene layers, a graphene layer and a substrate, and in a multilamellar graphene system are analyzed within the framework of the Lifshitz theory. This formulation hinges on a known form of the dielectric response function of an undoped or doped graphene sheet, assumed to be of a random phase approximation form. In the geometry of two apposed layers the separation dependence of the van der Waals-Casimir interaction for both types of graphene sheets is determined and compared with some well known limiting cases. In a multilamellar array the many-body effects are quantified and shown to increase the magnitude of the van der Waals-Casimir interactions.