Effects of spatial dispersion on the Casimir force between graphene sheets

Abstract

The asymptotic dispersion force F between two graphene sheets at a separation d is unusual: at T = 0 K, F ∼ Cd−p, where p = 4, unlike the 2D insulating (p = 5) or metallic (p = 7/2) cases. Here it is shown that these anomalous low-temperature properties of p are retained even when spatial dispersion (nonlocality) is included in the optical response properties of graphene. Furthermore, it is shown that the prefactor C is only weakly decreased (by <20%) upon spatial dispersion inclusion. For larger temperatures and nonzero chemical potential, such dispersion has even a lesser effect on the graphene/graphene force. The opening of a band gap in the graphene electronic structure, however, can cause larger sensitivity to spatial dispersion at elevated temperatures.