Effects of substrate and graphene surface roughness on graphene sheet plasmons - Lyon, Keenan; Miškovic, Z.L. (Nanoscale systems mathematical modeling, theory and applications, 2014)
We study the effects of roughness in a graphene layer that lies on a substrate with rough surface on the dynamic response of such a structure. Using an analytical expression for the dielectric function of flat graphene in the optical limit allows us to tackle the effects of roughness on the sheet plasmon in graphene. We first formulate a stochastic eigenvalue problem for the plasmon dispersion in terms of the roughness parameters that include both the auto– and the cross–correlation functions of graphene and the substrate surfaces. Using the projection operator methodwe reduce this problem to an integral equation for an effective dielectric function of graphene,which implies the existence of plasmon damping due to the roughness effects.