Environmental Effects on the Terahertz Surface Plasmons in Epitaxial Graphene

TL;DR

This study predicts low-frequency nonlocal surface plasmon excitations in multilayer graphene on a conducting substrate, revealing their dispersion, damping properties, and dependence on layer number and band gap, with potential coexistence of different quasiparticles.

Contribution

It introduces a theoretical model for surface plasmons in multilayer graphene on a substrate, highlighting their unique dispersion and the effect of layer number and band gap.

Findings

Surface plasmon-polaritons are undamped and lie below bulk plasmon modes.

The plasmon frequency depends on the number of graphene layers and their distance from the substrate.

No surface plasmon exists for more than approximately 7 layers.

Abstract

In this paper, we predict the existence of low-frequency nonlocal plasmon excitations at the vacuum-surface interface of a superlattice of $N$ graphene layers interacting with a thick conducting substrate. This is different from graphite which allows inter-layer hopping. A dispersion function is derived which incorporates the polarization function of the graphene monolayers (MLGs) and the dispersion function of a semi-infinite electron liquid at whose surface the electrons scatter specularly. We find that this surface plasmon-polariton is not damped by the particle-hole excitations (PHE's) or the bulk modes and separates below the continuum mini-band of bulk plasmon modes. For a conducting substrate with surface plasmon frequency $\omega_s=\omega_p/\sqrt{2}$, the surface plasmon frequency of the hybrid structure always lies below $\omega_s$. The intensity of this mode depends on the distance of the graphene layers from the surface of the conductor, the energy band gap between the valence and conduction bands of MLG and, most importantly, on the number of two-dimensional (2D) layers. Furthermore, the hybrid structure has no surface plasmon for a sufficiently large number ($N\stackrel{>}{\sim} 7$) of layers. The existence of two plasmons with different dispersion relations indicates that quasiparticles with different group velocity may coexist for various ranges of wavelength which is determined by the number of layers in the superlattice.