Influence of polar and metallic substrates on the surface plasmon in semi-infinite superlattice graphene structures

We investigated the role of polar and metallic substrates on the collective excitations of a semi-infinite layered graphene structures within the self-consistent field approximation. The surface plasmon dispersion in semi-infinite stack of graphene layers is indeed modified via Coulomb interaction with the metallic or polar substrate. At long wavelengths (q→0), these new surface-polariton are situated above bulk plasmon band of the stack with an infinite number of layers, and they have a very long lifetime. However at large momentum transfer the collective surface modes being sensitive to decay into a continuum plasmon band or by emitting an electron-hole pair excitation and thus are subject to Landau damping due of the relativistic Dirac nature of charge carriers in graphene.