Retarded interactions in Graphene systems

We first demonstrate how two-dimensional sheets are incorporated in the formalism for planar structures. Then we derive the interaction in the geometry of two free-standing graphene sheets and of one graphene sheet above a substrate. Numerical results are produced for the fully retarded interaction at 0 K and at room temperature for undoped and doped graphene. Additional results are given both for a gold substrate and for an ideal metal substrate.