Temperature-induced Coulomb excitations in rhombohedral 3D graphene

Low-energy electronic properties of ABC-stacked graphite are studied by the tight-binding model. There are linear and parabolic bands with and without degeneracy. They show strongly anisotropic dispersions. ABC-stacked grahite is a semimetal due to slight overlapping near the Fermi level beween conduction and valence bands. The interlayer interactions could change the energy dispersion, state degeneracy, and positions of band-crossing and band-edge state. Density of states exhibit a shoulder structure, owing to band-edge states near or at high symmetric points. Low-frequency Coulomb excitation properties with different transferred momenta (${\bf q}'$s) are further studied within the random phase approximation. The Landau dampings is too serious under the parallel transferred momentum (${\bf q}\perp \hat z$); therefore, it is impossible to observe the 3D optical plasmons. However, even for the perpendicular transferred momentum (${\bf q}\parallel \hat z$), the full assistance due to the thermal excitations is necessary to induce the collective charge oscillations along the $z$-axis. The height and position of temperature-induced plasmon peak in the energy loss spectrum are greatly enhanced by the increasing temperature, but weakly depend on the various transferred momenta. These features are very different from AA- and AB-stacked graphites.