Anisotropy of π-Plasmon Dispersion Relation of AA-Stacked Graphite

Abstract

The dispersion relation of the high energy optical π-plasmons of simple hexagonal intrinsic graphite was calculated within the self-consistent-field approximation. The plasmon frequency ω p is determined as functions of the transferred momentum q 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 transferred momentum is increased, the plasmon frequency strongly depends on its magnitude and direction (φ). With increasing angle, the dispersion relation within the hexagonal plane is gradually changed from quadratic to nearly linear form. There are many significant differences for the π-plasmon dispersion relations between 2D graphene and 3D AA-stacked graphite. They include q -and φ-dependence and π-plasmon bandwidth. This result reveals that interlayer interaction could enhance anisotropy of inplane π-plasmons. For chosen q , we also obtain the plasmon frequency as a function of q z and show that there is an upper bound on q z for plasmons to exist in graphite. Additionally, the group velocity for plasmon propagation along the perpendicular direction may be positive or negative depending on the choice of q . Consequently, the forward and backward propagation of π-plasmons in AA-stacked graphite in which the energy flow is respectively parallel or antiparallel to the transferred momentum, can be realized. The backward flowing resonance is an intrinsic property of AA-stacked graphite, arising from the energy band structure and the interlayer coupling.

Coulomb excitations for a short linear chain of metallic shells

“…(17). The calculation of the potential matrix elements of each interacting pair of S2DEGs is similar to our previous considerations [7,9].…”

“…For z−alignment, the azimuthal angle φ− is determined by the phases of the spherical harmonics in Eq. (17), so that only elements with M = M are non-zero, i.e. we obtain only two such elements.…”

“…These include the electrical, thermal, mechanical and chemical properties of graphite along the a, b and c directions [15] and the elastic properties of carbon nanotube bundles [16]. Also, the dispersion relation of the high-frequency optical π-plasmons for graphite was calculated by Chiu, et al, [17] and it was shown that the plasmon excitations depend on whether the momentum transfer is parallel or perpendicular to the hexagonal plane lying in the Brillouin zone. The anisotropic conductivity of epitaxial graphene on SiC was reported in Ref.…”

Electronic Transport and Optical Properties of Graphene

“…The generalized model can also be extensible to other layer stacked systems, i.e., AA-, AB-, ABC-stacked FLGs [87][88][89][90][91] and bulk graphite. [57,[92][93][94] Figure Captions …”

Effects of doping and bias voltage on the screening in AAA-stacked trilayer graphene

“…These materials, due to this staking order, have a special low energy band structure which is a composition of electron-doped, hole-doped and even undoped SLG-like band structures [13,14]. For some properties, these SLG-like bands behave like decoupled bands leading to many attractive properties which are different form that of SLG and also not been observed in the other graphene-based materials [14,15,16,17,18,19,20].…”