Graphene Plasmons In Interaction With A Surface

Recent experimental research on the plasmon spectrum of both carbon nanotubes and graphene has revealed a linear $\pi$ plasmon dispersion, which has been attributed to local field effects. Here we examine other possible sources of the linear plasmon dispersion found in graphene. In particular, we study the dispersion which may arise from the interaction of the intrinsic graphene plasmon ($\omega\sim q^{1/2}$) with the surface plasmon of a nearby thick substrate hosting a semi-infinite plasma.