Universal nature of collective plasmonic excitations in finite 1D carbon-based nanostructures

Abstract

Tomonaga-Luttinger (T-L) theory predicts collective plasmon resonances in 1-D nanostructure conductors of finite length, that vary roughly in inverse proportion to the length of the structure. In-depth quantitative understanding of such resonances which have not been clearly identified in experiments so far, would be invaluable for future generations of nano-photonic and nano-electronic devices that employ 1-D conductors. Here we provide evidence of the plasmon resonances in a number of representative 1-D finite carbon-based nanostructures using first-principle computational electronic spectroscopy studies. Our special purpose real-space/real-time all-electron Time-Dependent Density-Functional Theory (TDDFT) simulator can perform excited-states calculations to obtain correct frequencies for known optical transitions, and capture various nanoscopic effects including collective plasmon excitations. The presence of 1-D plasmons is universally predicted by the various numerical experiments, which also demonstrate a phenomenon of resonance splitting. For the metallic carbon nanotubes under study, the plasmons are expected to be related to the T-L plasmons of infinitely long 1-D structures.

From Fundamental First-Principle Calculations to NanoEngineering Applications: Review of the NESSIE project

“…In Ref. [99], NESSIE has been used to provide evidence of the plasmon resonances (collective electron excitations) in a number of representative short 1D finite carbon-based nanostructures using real-time TDDFT simulations. The simulated systems ranged from small molecules such as C 2 H 2 to various carbon nanostructures that are equivalent to 1D conductors with finite lengths, including: carbon chains, narrow armchair and zigzag graphene nanoribbons (i.e.…”

“…The chief signature of 1D plasmons is a high-frequency excitation that is inversely proportional to the length of the conductor. In particular, it was shown that metallic 1D CNTs can be well described with the Tomonaga-Luttinger theory [99], [120]- [124]. The plasmon velocity is expected to reach an asymptotic value (up to 3 to 5 times the single particle Fermi velocity) when the simulations are extended to tens of unit cells, such as very long CNT that become relevant for THz spectroscopy.…”

“…Since the reported preliminary work on short CNT [99] (about 5 unit-cells), NESSIE has been upgraded to simulate large-scale atomistic systems by taking advantage of new high performance computing techniques such as the muffin-DD solver presented and discussed in Figures 2 and 3. This allelectron real-space and real-time TDDFT framework is now capable to simulate very large structures (up to tens of unit cells for CNT -from hundred atoms to few thousands), and lead to more relevant predicted data of the plasmonic effects for 1D systems.…”

“…charge oscillations at ω). One possible way to visualize δn(ω, r) is by applying a sinusoidal excitation at a given frequency of interest, waiting for the induced dipole moment to reach a steady state where it oscillates at ω, and plotting the 4D data when the dipole reaches a maximum and a minimum [99]. Another more efficient approach consists of computing δn(ω, r) directly following the same procedure used for deriving the dipole moment in ( 14) and (16), which leads to:…”

Approaching the quantum limit for plasmonics: linear atomic chains

“…Plasmons are wavelike excitations of oscillating charge density that arise in noble metals with a high density of free conduction electrons [1]. They may also occur in other systems with mobile charges such as long-chain molecules [2][3][4], atomic chains on surfaces [5][6][7][8][9][10][11] carbon nanotubes [12,13], doped graphene [14], other complex molecules [15][16][17][18], and one-dimensional solids [19]. In extended one-dimensional systems, plasmons are charge excitations of the long-studied Luttinger liquid [20].…”