Dispersion interaction of two graphene sheets

The Casimir method for determining the dispersive force by varying zero vacuum energy fluctuations is applied to two graphene sheets in the approximation of the Drude model for surface conductivity. As an alternative, the Van Kampen summation method is used. The force is determined for small and for large distances between the sheets. The results of both models are quite similar. Precisely, at large distances, the attractive force decreases inversely proportional to the fourth power of the distance. At short distances, the force is a finite attractive one. With a small chemical potential, the force can have a minimum at distances of the order of 0.3 nm, then increases, reaches a maximum at distances of the order of 200 nm, and at large distances decreases inversely proportional to the fourth power of the distance. At a chemical potential of significantly more than 1 eV, a minimum is not observed.