  We study localized plasmonic excitations in bilayer graphene (BLG) nanodisks,
comparing AA-stacked and AB-stacked BLG and contrasting the results to the case
of two monolayers without electronic hybridization. The electrodynamic response
of the BLG electron gas is described in terms of a spatially homogeneous
surface conductivity, and an efficient alternative two-dimensional
electrostatic approach is employed to carry out all the numerical calculations
of plasmon resonances. Due to a unique electronic band structures, the
resonance frequency of the traditional dipolar plasmonic mode in the AA-stacked
BLG nanodisk is roughly doping independent in the low-doping regime, while the
mode is highly damped as the Fermi level approaches the interlayer hopping
energy $\gamma$ associated with tunneling of electrons between the two layers.
In addition to the traditional dipolar mode, we find that the AB-stacked BLG
nanodisk also hosts a new plasmonic mode with energy larger than $\gamma$. This
mode can be tuned by either the doping level or structural size, and
furthermore, this mode can dominate the plasmonic response for realistic
structural conditions.
