Casimir forces and graphene sheets

The Casimir force between two infinitely thin parallel sheets in a setting of N such sheets is found. The finite two-dimensional conductivities, which describe the dispersive and absorptive properties of each sheet, are taken into account, whereupon the theory is applied to interacting graphenes. By exploring similarities with in-plane optical spectra for graphite, the conductivity of graphene is modeled as a combination of Lorentz-type oscillators. We find that the graphene transparency and the existence of a universal constant conductivity e(2)/(4h) result in the graphene/graphene Casimir interaction at large separations to have the same distance dependence as the one for perfect conductors but with much smaller magnitude. The Casimir force is also studied when the graphene system is above a substrate or immersed in a medium. It is found that the response properties of the environmental materials can strongly affect the graphene interaction.