Casimir effects in systems containing 2D layers such as graphene and 2D electron gases

We present a variety of methods to derive the Casimir interaction in planar systems containing 2D layers. Examples where this can be of use is graphene, graphene-like layers and 2D electron gases. We present results for two free standing layers and for one layer above a substrate. The results can easily be extended to systems with a larger number of layers.