Anisotropy of $\pi$-plasmon Dispersion Relation of AA-stacked Graphite

The dispersion relation of optical $\pi$-plasmons of simple hexagonal intrinsic graphite was calculated within the self-consistent-field approximation. The plasmon frequency $\omega_p$ is determined as functions of the wave vector $\textbf{q}_\parallel$ along the hexagonal plane in the Brillouin zone and its perpendicular component $q_z$. These plasmons are isotropic within the plane in the long wavelength limit. As the in-plane wave vector is increased, the plasmon frequency strongly depends on its magnitude and direction ($\phi$). Our results reveal that interlayer interaction could enhance anisotropy of in-plane $\pi$-plasmons. The group velocity for plasmon propagation along the perpendicular direction may be positive or negative depending on the choice of in-plane wave vector.