Eur. Phys. J. B (2012) 85: 365
https://doi.org/10.1140/epjb/e2012-30741-6

Regular Article

Effects of spatial dispersion on the Casimir force between graphene sheets

¹ Department of Physics, University of South Florida, 33620 Tampa, FL, USA
² Department of Physics, North Carolina Central University, 27707 Durham, NC, USA
³ Micro and Nanotechnology Centre, Griffith University, Nathan, 4111 Queensland, Australia

^a e-mail: lmwoods@usf.edu

Received: 11 April 2012
Received in final form: 10 August 2012
Published online: 5 November 2012

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.