Figure 4: Plasmon dispersion for N = 7 graphene layers on a conducting substrate.
From: Plasmon Excitations of Multi-layer Graphene on a Conducting Substrate
As in Fig. 3, the layers in (a–d) are gapless, whereas in (e–h) each layer has a gap Δ = 0.6μ. The inter-layer separation is 
. The first layer is at distances a1kF = 0.2 from the surface of the semi-infinite conductor. If the gap or number of layers is increased, the lowest branch does not re-appear for large q||.
