  The layered graphene systems exhibit the rich and unique excitation spectra
arising from the electron-electron Coulomb interactions. The generalized
tight-binding model is developed to cover the planar/buckled/cylindrical
structures, specific lattice symmetries, different layer numbers, distinct
configurations, one-three dimensions, complicated intralayer and interlayer
hopping integrals, electric field, magnetic quantization; any temperatures and
dopings simultaneously. Furthermore, we modify the random-phase approximation
to agree with the layer-dependent Coulomb potentials with the Dyson equation,
so that these two methods can match with other under various external fields.
The electron-hole excitations and plasmon modes are greatly diversified by the
above-mentioned critical factors; that is, there exist the diverse (momentum.
frequency)-related phase diagrams. They provide very effective deexcitation
scatterings and thus dominate the Coulomb decay rates. Graphene, silicene and
germanene might quite differ from one another in Coulomb excitations and decays
because of the strength of spin-orbital coupling. Part of theoretical
predictions have confirmed the experimental measurements, and most of them
require the further examinations. Comparisons with the other models are also
made in detail.
