Local density of states at zigzag edges of carbon nanotubes and graphene

Ken Ichi Sasaki, Kentaro Sato, Riichiro Saito, Jie Jiang, Seiichiro Onari, Yukio Tanaka

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

The electron-phonon matrix element for edge states of carbon nanotubes and graphene at zigzag edges is calculated for obtaining renormalized energy dispersion of the edge states. Self-energy correction by electron-phonon interaction contributes to the energy dispersion of edge states whose energy bandwidth is similar to phonon energy. Since the energy uncertainty of the edge state is larger than temperature, we conclude that the single-particle picture of the edge state is not appropriate when the electron-phonon interaction is taken into account. The longitudinal acoustic phonon mode contributes to the matrix element through the on-site deformation potential because the wave function of the edge state has an amplitude only on one of the two sublattices. The on-site deformation potentials for the longitudinal and in-plane tangential optical phonon modes are enhanced at the boundary. The results of local density of states are compared with the recent experimental data of scanning tunneling spectroscopy.

Original languageEnglish
Article number235430
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume75
Issue number23
DOIs
Publication statusPublished - Jun 20 2007
Externally publishedYes

Fingerprint

Electron-phonon interactions
Carbon Nanotubes
Graphite
Graphene
Carbon nanotubes
graphene
carbon nanotubes
Wave functions
Electron energy levels
Acoustics
Spectroscopy
Scanning
Bandwidth
electron phonon interactions
Electrons
energy
Temperature
matrices
sublattices
wave functions

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

Local density of states at zigzag edges of carbon nanotubes and graphene. / Sasaki, Ken Ichi; Sato, Kentaro; Saito, Riichiro; Jiang, Jie; Onari, Seiichiro; Tanaka, Yukio.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 75, No. 23, 235430, 20.06.2007.

Research output: Contribution to journalArticle

Sasaki, Ken Ichi ; Sato, Kentaro ; Saito, Riichiro ; Jiang, Jie ; Onari, Seiichiro ; Tanaka, Yukio. / Local density of states at zigzag edges of carbon nanotubes and graphene. In: Physical Review B - Condensed Matter and Materials Physics. 2007 ; Vol. 75, No. 23.
@article{1acc8a13cd654cb4aab2ec2bbc95bf93,
title = "Local density of states at zigzag edges of carbon nanotubes and graphene",
abstract = "The electron-phonon matrix element for edge states of carbon nanotubes and graphene at zigzag edges is calculated for obtaining renormalized energy dispersion of the edge states. Self-energy correction by electron-phonon interaction contributes to the energy dispersion of edge states whose energy bandwidth is similar to phonon energy. Since the energy uncertainty of the edge state is larger than temperature, we conclude that the single-particle picture of the edge state is not appropriate when the electron-phonon interaction is taken into account. The longitudinal acoustic phonon mode contributes to the matrix element through the on-site deformation potential because the wave function of the edge state has an amplitude only on one of the two sublattices. The on-site deformation potentials for the longitudinal and in-plane tangential optical phonon modes are enhanced at the boundary. The results of local density of states are compared with the recent experimental data of scanning tunneling spectroscopy.",
author = "Sasaki, {Ken Ichi} and Kentaro Sato and Riichiro Saito and Jie Jiang and Seiichiro Onari and Yukio Tanaka",
year = "2007",
month = "6",
day = "20",
doi = "10.1103/PhysRevB.75.235430",
language = "English",
volume = "75",
journal = "Physical Review B-Condensed Matter",
issn = "1098-0121",
publisher = "American Physical Society",
number = "23",

}

TY - JOUR

T1 - Local density of states at zigzag edges of carbon nanotubes and graphene

AU - Sasaki, Ken Ichi

AU - Sato, Kentaro

AU - Saito, Riichiro

AU - Jiang, Jie

AU - Onari, Seiichiro

AU - Tanaka, Yukio

PY - 2007/6/20

Y1 - 2007/6/20

N2 - The electron-phonon matrix element for edge states of carbon nanotubes and graphene at zigzag edges is calculated for obtaining renormalized energy dispersion of the edge states. Self-energy correction by electron-phonon interaction contributes to the energy dispersion of edge states whose energy bandwidth is similar to phonon energy. Since the energy uncertainty of the edge state is larger than temperature, we conclude that the single-particle picture of the edge state is not appropriate when the electron-phonon interaction is taken into account. The longitudinal acoustic phonon mode contributes to the matrix element through the on-site deformation potential because the wave function of the edge state has an amplitude only on one of the two sublattices. The on-site deformation potentials for the longitudinal and in-plane tangential optical phonon modes are enhanced at the boundary. The results of local density of states are compared with the recent experimental data of scanning tunneling spectroscopy.

AB - The electron-phonon matrix element for edge states of carbon nanotubes and graphene at zigzag edges is calculated for obtaining renormalized energy dispersion of the edge states. Self-energy correction by electron-phonon interaction contributes to the energy dispersion of edge states whose energy bandwidth is similar to phonon energy. Since the energy uncertainty of the edge state is larger than temperature, we conclude that the single-particle picture of the edge state is not appropriate when the electron-phonon interaction is taken into account. The longitudinal acoustic phonon mode contributes to the matrix element through the on-site deformation potential because the wave function of the edge state has an amplitude only on one of the two sublattices. The on-site deformation potentials for the longitudinal and in-plane tangential optical phonon modes are enhanced at the boundary. The results of local density of states are compared with the recent experimental data of scanning tunneling spectroscopy.

UR - http://www.scopus.com/inward/record.url?scp=34347388212&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34347388212&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.75.235430

DO - 10.1103/PhysRevB.75.235430

M3 - Article

AN - SCOPUS:34347388212

VL - 75

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 23

M1 - 235430

ER -