Plasmons in layered structures including graphene

We investigate the optical properties of layered structures with graphene at the interface for arbitrary linear polarization at finite temperature including full retardation by working in the Weyl gauge. As a special case, we obtain the full response and the related dielectric function of a layered structure with two interfaces. We apply our results to discuss the longitudinal plasmon spectrum of several single- and double-layer devices such as systems with finite and zero electronic densities. We further show that a nonhomogeneous dielectric background can shift the relative weight of the in-phase and out-of-phase modes, and discuss how the plasmonic mode of the upper layer can be tuned into an acoustic mode with a specific sound velocity.