Interaction Energy between Graphene and a Silicon Substrate Using Pairwise Summation of the Lennard-Jones Potential

We consider the computation of a long-range interaction energy between a single graphene sheet and a silicon substrate, which arises from vacuum fluctuations. The interaction energy obtained by summation of the Lennard-Jones potential between a carbon atom in a single graphene sheet and a silicon atom is compared with the dispersion energy (Casimir energy) obtained by combining the Lifshitz theory and the Dirac model for graphene. Deviation of the pairwise summation of the Lennard-Jones potential from the Casimir energy is corrected by adding a power-function term, whose coefficient depends on the distance between atoms. We also consider the interaction between a graphene sheet and a silicon dioxide substrate.