Density-wave instability and impurity screening in graphene based double-layer structures

In this study, we investigate the density-wave instability and impurity screening in graphene-based double-layer structures. We assume that at least one of two layers is graphene, while the second layer could be made of graphene, conventional two-dimensional electron gas, or any other two-dimensional structure. We calculate the static dielectric function of this graphene-based double-layer structure whitin the random phase approximation, and look for the possibility of density-wave instability, changing different system parameters like the electronic density and layer spacing between two layers. In this investigation we have not seen any instability in double-layer structures consisting of coupled layers of graphene, the 2D electron gas and the gapped graphene. Finally, using static dielectric function and considering a charged impurity placed in the first layer, we show that how this impurity is screened in the first and second layers.