Edge-dependent reflection and inherited fine structure of higher-order plasmons in graphene nanoribbons

Kåre Obel Wedel*, N. Asger Mortensen, Kristian S. Thygesen, Martijn Wubs

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

We investigate higher-order plasmons in graphene nanoribbons, and we present how electronic edge states and wave-function fine structure influence the graphene plasmons. Based on nearest-neighbor tight-binding calculations, we find that a standing-wave model based on nonlocal bulk plasmon dispersion is surprisingly accurate for armchair ribbons of widths even down to a few nanometers, and we determine the corresponding phase shift upon edge reflection and an effective ribbon width. Wider zigzag ribbons exhibit a similar phase shift, whereas the standing-wave model describes few-nanometer zigzag ribbons less satisfactorily, to a large extent because of their edge states. We directly confirm that also the larger broadening of plasmons for zigzag ribbons is due to their edge states. Furthermore, we report a prominent fine structure in the induced charges of the ribbon plasmons, which for armchair ribbons follows the electronic wave-function oscillations induced by intervalley coupling. Interestingly, the wave-function fine structure is also found in our analogous density-functional theory calculations, and both these and tight-binding numerical calculations are explained quite well with analytical Dirac theory for graphene ribbons.

Original languageEnglish
Article number045411
JournalPhysical Review B
Volume99
Issue number4
Number of pages10
ISSN2469-9950
DOIs
Publication statusPublished - 2019

Cite this

@article{d3c6ff2715b14095a98ea2d86980af6a,
title = "Edge-dependent reflection and inherited fine structure of higher-order plasmons in graphene nanoribbons",
abstract = "We investigate higher-order plasmons in graphene nanoribbons, and we present how electronic edge states and wave-function fine structure influence the graphene plasmons. Based on nearest-neighbor tight-binding calculations, we find that a standing-wave model based on nonlocal bulk plasmon dispersion is surprisingly accurate for armchair ribbons of widths even down to a few nanometers, and we determine the corresponding phase shift upon edge reflection and an effective ribbon width. Wider zigzag ribbons exhibit a similar phase shift, whereas the standing-wave model describes few-nanometer zigzag ribbons less satisfactorily, to a large extent because of their edge states. We directly confirm that also the larger broadening of plasmons for zigzag ribbons is due to their edge states. Furthermore, we report a prominent fine structure in the induced charges of the ribbon plasmons, which for armchair ribbons follows the electronic wave-function oscillations induced by intervalley coupling. Interestingly, the wave-function fine structure is also found in our analogous density-functional theory calculations, and both these and tight-binding numerical calculations are explained quite well with analytical Dirac theory for graphene ribbons.",
author = "Wedel, {K{\aa}re Obel} and Mortensen, {N. Asger} and Thygesen, {Kristian S.} and Martijn Wubs",
year = "2019",
doi = "10.1103/PhysRevB.99.045411",
language = "English",
volume = "99",
journal = "Physical Review B (Condensed Matter and Materials Physics)",
issn = "1098-0121",
publisher = "American Physical Society",
number = "4",

}

Edge-dependent reflection and inherited fine structure of higher-order plasmons in graphene nanoribbons. / Wedel, Kåre Obel; Mortensen, N. Asger; Thygesen, Kristian S.; Wubs, Martijn.

In: Physical Review B, Vol. 99, No. 4, 045411, 2019.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Edge-dependent reflection and inherited fine structure of higher-order plasmons in graphene nanoribbons

AU - Wedel, Kåre Obel

AU - Mortensen, N. Asger

AU - Thygesen, Kristian S.

AU - Wubs, Martijn

PY - 2019

Y1 - 2019

N2 - We investigate higher-order plasmons in graphene nanoribbons, and we present how electronic edge states and wave-function fine structure influence the graphene plasmons. Based on nearest-neighbor tight-binding calculations, we find that a standing-wave model based on nonlocal bulk plasmon dispersion is surprisingly accurate for armchair ribbons of widths even down to a few nanometers, and we determine the corresponding phase shift upon edge reflection and an effective ribbon width. Wider zigzag ribbons exhibit a similar phase shift, whereas the standing-wave model describes few-nanometer zigzag ribbons less satisfactorily, to a large extent because of their edge states. We directly confirm that also the larger broadening of plasmons for zigzag ribbons is due to their edge states. Furthermore, we report a prominent fine structure in the induced charges of the ribbon plasmons, which for armchair ribbons follows the electronic wave-function oscillations induced by intervalley coupling. Interestingly, the wave-function fine structure is also found in our analogous density-functional theory calculations, and both these and tight-binding numerical calculations are explained quite well with analytical Dirac theory for graphene ribbons.

AB - We investigate higher-order plasmons in graphene nanoribbons, and we present how electronic edge states and wave-function fine structure influence the graphene plasmons. Based on nearest-neighbor tight-binding calculations, we find that a standing-wave model based on nonlocal bulk plasmon dispersion is surprisingly accurate for armchair ribbons of widths even down to a few nanometers, and we determine the corresponding phase shift upon edge reflection and an effective ribbon width. Wider zigzag ribbons exhibit a similar phase shift, whereas the standing-wave model describes few-nanometer zigzag ribbons less satisfactorily, to a large extent because of their edge states. We directly confirm that also the larger broadening of plasmons for zigzag ribbons is due to their edge states. Furthermore, we report a prominent fine structure in the induced charges of the ribbon plasmons, which for armchair ribbons follows the electronic wave-function oscillations induced by intervalley coupling. Interestingly, the wave-function fine structure is also found in our analogous density-functional theory calculations, and both these and tight-binding numerical calculations are explained quite well with analytical Dirac theory for graphene ribbons.

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DO - 10.1103/PhysRevB.99.045411

M3 - Journal article

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VL - 99

JO - Physical Review B (Condensed Matter and Materials Physics)

JF - Physical Review B (Condensed Matter and Materials Physics)

SN - 1098-0121

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