Plasmonic eigenmodes in individual and bow-tie graphene nanotriangles

Abstract

In classical electrodynamics, nanostructured graphene is commonly modeled by the computationally demanding problem of a three-dimensional conducting film of atomic-scale thickness. Here, we propose an efficient alternative two-dimensional electrostatic approach where all calculation procedures are restricted to the graphene sheet. Furthermore, to explore possible quantum effects, we perform tight-binding calculations, adopting a random-phase approximation. We investigate multiple plasmon modes in 20 nm equilateral triangles of graphene, treating the optical response classically as well as quantum mechanically. Compared to the classical plasmonic spectrum which is “blind” to the edge termination, we find that the quantum plasmon frequencies exhibit blueshifts in the case of armchair edge termination of the underlying atomic lattice, while redshifts are found for zigzag edges. Furthermore, we find spectral features in the zigzag case which are associated with electronic edge states not present for armchair termination. Merging pairs of triangles into dimers, plasmon hybridization leads to energy splitting that appears strongest in classical calculations while splitting is lower for armchair edges and even more reduced for zigzag edges. Our various results illustrate a surprising phenomenon: Even 20 nm large graphene structures clearly exhibit quantum plasmonic features due to atomic-scale details in the edge termination.

Classical and quantum plasmonics in graphene nanodisks: Role of edge states

“…This underscores the accuracy of a hydrodynamic description, since RPA@Dirac IM neglects the existence of edge states, and thus, at large radii, is modified primarily by nonlocal effects. Moreover, through this, we qualitatively explain the blueshift predicted by RPA@TB in armchair nanostructures [39,40] as a hydrodynamic shift.…”

Graphene-plasmon polaritons: From fundamental properties to potential applications

“…As an example, Cai et al presented their bottom-up approach to control the graphene nanoribbons with atomic resolution [113]. When the size of graphene structures becomes smaller and smaller, we eventually also need to be concerned with atomic-scale details, such as quantum mechanical effects associated with electronic edge states inevitably hosted by zigzag terminations of the graphene lattice [36,37,116], which shift and broaden the plasmon resonances.…”

Quantum Effects in the Nonlinear Response of Graphene Plasmons

“…However, this classical approach neglects nonlocal, finite-size, and atomistic (e.g., edge termination) effects, all of which have been found to play crucial roles in describing both the linear [57][58][59] and nonlinear [51,52] optical response of graphene structures with small (∼ 10 nm) features. Here we reveal strong finite-size and atomistic effects in the nonlinear response of graphene nanoribbons and nanoislands, predicted to take place from a realistic, QM description of these structures, beyond classical theory, which can produce dramatically different results for structure sizes up to a few tens of nanometers.…”