Full symmetry, optical activity, and potentials of single-wall and multiwall nanotubes

Damnjanović, Milan; Milošević, I.; Vuković, T.; Sredanović, R.

doi:10.1103/physrevb.60.2728

Cited by 292 publications

(273 citation statements)

References 26 publications

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“…All the geometrical symmetries of chiral (n 1 , n 2 ), zigzag (n, 0) and armchair (n, n) SWCT (C, Z and A tubes for short) are gathered in the line groups 4 (the factorized and the international notation are given):…”

Section: Introductionmentioning

confidence: 99%

Carbon nanotubes band assignation, topology, Bloch states, and selection rules

2002

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Various properties of the energy band structures (electronic, phonon, etc.), including systematic band degeneracy, sticking and extremes, following from the full line group symmetry of the singlewall carbon nanotubes are established. The complete set of quantum numbers consists of quasi momenta (angular and linear or helical) and parities with respect to the z-reversal symmetries and, for achiral tubes, the vertical plane. The assignation of the electronic bands is performed, and the generalized Bloch symmetry adapted eigen functions are derived. The most important physical tensors are characterized by the same set of quantum numbers. All this enables application of the presented exhaustive selection rules. The results are discussed by some examples, e.g. allowed interband transitions, conductivity, Raman tensor, etc.

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Section: Introductionmentioning

confidence: 99%

Carbon nanotubes band assignation, topology, Bloch states, and selection rules

2002

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“…One-photon excitations (solid blue line) couple to excitonic states with odd (u) symmetry with respect to π rotations about the U-axis. The Uaxis is perpendicular to the tube axis through the center of the C hexagons [24]. (1) and (2) The important observation is that -for each tube -one finds a maximum in the luminescence intensity at an excitation wavelength that is far above the emission wavelength, but significantly smaller than twice the emission wavelength.…”

Section: Introductionmentioning

confidence: 99%

“…In carbon nanotubes, one expects that for each allowed interband transition there exist a series of transitions to optically active exciton states having odd (u) symmetry with respect to rotations by π about the nanotube U-axis [8,24,25]. Twophoton spectroscopy, on the other hand, couples to the otherwise optically inactive even (g) states.…”

Section: Introductionmentioning

confidence: 99%

Optical spectroscopy of single‐walledcarbon nanotubes: From excitonic effects towards control of the radiative lifetime

Pomraenke¹,

Vasa²,

Lienau³

2008

Physica Status Solidi (b)

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We have recently studied excitonic effects on the optical properties of single‐walled carbon nanotubes by means of two‐photon spectroscopy and time‐resolved photoluminescence spectroscopy. For nanotubes with diameters between 6.8 Å and 9.0 Å, the two‐photon spectra give evidence for large binding energies between 300 meV to 400 meV. Theoretical simulations of these spectra indicate that the lowest energy exciton state in nanotubes is an optically dark exciton, which has profound implications on the luminescence yield and exciton dynamics in single‐walled nanotubes. Indeed, time‐resolved photoluminescence measurements of individual nanotubes reveal low quantum yields and rather short exciton lifetimes ranging from 10 ps to 200 ps, which are affected by exciton relaxation between bright and dark states and non‐radiative exciton recombination. These results suggest that a control of the radiative lifetime of nanotube excitons may be a viable strategy for enhancing their luminescence yield. Here, we propose that exciton‐coupling to surface plasmon polaritons in metallic nanostructures may result in a substantial enhancement of the radiative exciton decay rate. Two‐photon luminescence excitation spectra of single‐walled carbon nanotubes. The luminescence intensity is plotted as a function of excitation and detection wavelength. The various two‐photon resonances are assigned to nanotube species with different chiral indices (n,m), as indicated in the figure. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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“…Nanotubes are highly symmetric, to the extent that their symmetry group, completely defi ned through the line groups [3], generates the whole nanotube from a single atom. Th us, only symmetry and properties of the atom determine all properties of the nanotube.…”

Section: Carbon Nanotubes and Symmetrymentioning

confidence: 99%

Symmetry of quasi one-dimensional systems: line groups and applications

Damnjanović

2014

Europhysics News

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Full symmetry, optical activity, and potentials of single-wall and multiwall nanotubes

Cited by 292 publications

References 26 publications

Carbon nanotubes band assignation, topology, Bloch states, and selection rules

Carbon nanotubes band assignation, topology, Bloch states, and selection rules

Optical spectroscopy of single‐walledcarbon nanotubes: From excitonic effects towards control of the radiative lifetime

Symmetry of quasi one-dimensional systems: line groups and applications

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