▎ 摘　　要

The non-retarded Casimir interaction (van der Waals interaction) between two freestanding graphene sheets as well as between a graphene sheet and a substrate is determined. We present several different derivations of the interaction. An exact analytical expression is given for the dielectric function of graphene along the imaginary frequency axis within the random phase approximation for arbitrary frequency, wave vector, and doping. Copyright (C) EPLA, 2011