Figure 2: Plasmon excitation spectra for a semi-infinite conductor interacting through the Coulomb interaction with N = 2 monolayer graphene sheets located at chosen distances from the surface.
From: Plasmon Excitations of Multi-layer Graphene on a Conducting Substrate
The left-hand panels (a,c,e) give density plots of the inverse dispersion function 
with peaks corresponding to the plasmon modes. The right panels (b,d,f) show the numerical solutions for the Landau damped (dashed blue lines) and undamped (red curves) plasmon branches. The plots show results for various distances between the surface and the layers: a1kF = 2.0, 0.2 and 0.5, respectively. The second layer is placed at a distance a2, equal to twice as large as a1. All the plots are provided for extrinsic graphene (doped) with zero energy bandgap.
