Collective modes of doped two-dimensional crystalline materials, namely graphene, MoS$_2$ and phosphorene, both monolayer and bilayer structures, are explored using the density functional theory simulations together with the random phase approximation. The many-body dielectric functions of the materials are calculated using an {it ab initio} based model involving material-realistic physical properties. Having calculated the electron energy-loss, we calculate the collective modes of each material considering the in-phase and out-of-phase modes for bilayer structures. Furthermore, owing to many band structures and intreband transitions, we also find high-energy excitations in the systems. We explain that the material-specific dielectric function considering the polarizability of the crystalline material such as MoS$_2$ are needed to obtain realistic plasmon dispersions. For each material studied here, we find different collective modes and describe their physical origins.
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