Analytical Calculations on Low-Frequency Excitations in AA-Stacked Bilayer Graphene

The bare response functions and the dielectric function tensor in AA-stacked bilayer graphene are investigated analytically within the tight-binding model and the random-phase approximation. They are dominated by the interlayer atomic interactions. The main features of the single-particle excitations are associated with the Fermi-momentum states. The intralayer and interlayer polarization functions possess two kinds of simple relations, which correspond to the electronic excitations between different-pair and same-pair linear energy bands, respectively. There exist optical and acoustic plasmons. At long wavelengths, the plasmon frequencies show a different dependence on the transferred momentum. These frequency dispersions calculated from the vanishing real-part determinant of the dielectric function tensor are consistent with those obtained from the numerical loss functions. The analytical response functions are useful in understanding other many-body effects.