Plasmonic eigenmodes in individual and bow-tie graphene nanotriangles

TL;DR

This paper investigates plasmonic modes in graphene nanotriangles, revealing quantum edge effects and hybridization phenomena, using a novel two-dimensional electrostatic model and quantum calculations for different edge terminations.

Contribution

It introduces an efficient 2D electrostatic approach for studying graphene plasmons and compares classical and quantum effects, highlighting edge-dependent spectral shifts and quantum edge states.

Findings

Quantum plasmon frequencies show blueshifts for armchair edges.

Zigzag edges exhibit redshifts and unique edge states.

Plasmon hybridization in dimers causes energy splitting, influenced by edge type.

Abstract

Serving as a new two-dimensional plasmonic material, graphene has stimulated an intensive study of its optical properties which benefit from the unique electronic band structure of the underlying honeycomb lattice of carbon atoms. 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 the calculation procedures are restricted to the plane of the graphene sheet. To explore possible quantum effects, we perform tight-binding calculations, adopting a random-phase approximation. We investigate the multiple plasmon modes in triangles of graphene, treating the optical response classically as well as quantum mechanically in the case of both armchair and zigzag edge termination of the underlying atomic lattice. 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, 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 such triangles into dimers, the plasmon hybridization leads to energy splitting in accordance with plasmon-hybridization theory, with a lower energy for the antisymmetric modes and a smaller splitting for modes with less confinement to the gap region. The hybridization appears strongest in classical calculations while the 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.