  The layer-based random-phase approximation is further developed to
investigate electronic excitations in tri-layer ABC-stacked graphene. All the
layer-dependent atomic interactions and Coulomb interactions are included in
the dynamic charge screening. There exist rich and unique (momentum,
frequency)-excitation phase diagrams, in which the complex single-particle
excitations and five kinds of plasmon modes, are dominated by the unusual
energy bands and doping carrier densities. The latter frequently experience the
significant Landau damping due to the former, leading to the
coexistence/destruction in the energy loss spectra. Specifically, the
dispersion of the only acoustic plasmon in pristine case is dramatically
changed from linear into quadratic even at very low doping.
