Recent Progress on Nonlocal Graphene/Surface Plasmons

Abstract

We review recent experimental and theoretical studies of the non-local plasmon dispersion relations of both single and double layers of graphene which are Coulomb-coupled to a thick conducting medium. High-resolution electron energy loss spectroscopy (HREELS) was employed in the investigations. A mean-field theory (R.P.A.) formulation was used to simulate and explain the experimental results, with the undamped plasmon excitation spectrum calculated for arbitrary wave number. Our numerical calculations show that when the separation a between a graphene layer and the surface is less than a critical value ac = 0.4kF−1, the lower acoustic plasmon is overdamped. This result seems to explain the experimentally observed behavior for the plasmon mode intensity as a function of wave vector. The damping, as well as the critical distance, changes in the presence of an energy bandgap for graphene. We also report similar damping features of the plasmon modes for a pair of graphene layers. However, the main difference arising in the case when there are two layers is that if the separation between the layer nearest the surface and the surface is less than ac, then both the symmetric and antisymmetric modes become damped, in different ranges of wave vector.