Exciton absorption of perpendicularly polarized light in carbon nanotubes

Uryu, Seiji; Ando, Tsuneya

doi:10.1103/physrevb.74.155411

Cited by 91 publications

(114 citation statements)

References 44 publications

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“…2b). This shows that the observed peaks can be ascribed to three excitonic transitions E ii between sub-bands of same index i (refs 26,[26][27][28][29][30]33).…”

Section: Resultsmentioning

confidence: 99%

“…Each of these optical resonances is referred to as S ij or M ij , depending on the nature of the nanotube (S for semiconducting and M for metallic) and the corresponding valence (i) and conduction (j) sub-band in the single-particle band model. Selection rules in SWNTs requires that incident light polarized parallel to the tube main axis probes transitions between sub-bands of the same index (i ¼ j), and that cross-polarized light addresses transitions between sub-bands with unitary index difference (|i À j| ¼ 1) 29,30 . More precisely, each sub-band i shows Rydberg-like exciton states, which are composed of 4 singlet and 12 triplet states 30 .…”

Section: Resultsmentioning

confidence: 99%

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Direct measurement of the absolute absorption spectrum of individual semiconducting single-wall carbon nanotubes

et al. 2013

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The optical properties of single-wall carbon nanotubes are very promising for developing novel opto-electronic components and sensors with applications in many fields. Despite numerous studies performed using photoluminescence or Raman and Rayleigh scattering, knowledge of their optical response is still partial. Here we determine using spatial modulation spectroscopy, over a broad optical spectral range, the spectrum and amplitude of the absorption cross-section of individual semiconducting single-wall carbon nanotubes. These quantitative measurements permit determination of the oscillator strength of the different excitonic resonances and their dependencies on the excitonic transition and type of semiconducting nanotube. A non-resonant background is also identified and its cross-section comparable to the ideal graphene optical absorbance. Furthermore, investigation of the same single-wall nanotube either free standing or lying on a substrate shows large broadening of the excitonic resonances with increase of oscillator strength, as well as stark weakening of polarization-dependent antenna effects, due to nanotube-substrate interaction.

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“…2b). This shows that the observed peaks can be ascribed to three excitonic transitions E ii between sub-bands of same index i (refs 26,[26][27][28][29][30]33).…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Direct measurement of the absolute absorption spectrum of individual semiconducting single-wall carbon nanotubes

et al. 2013

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“…However, due to the depolarization effect, these perpendicular transitions are expected to be heavily suppressed, 41 although excitonic effects are predicted to retain this transition as a well-defined peak in absorption at a renormalized energy. 49 Subsequently, Jiang et al, 50 using the tight-binding method, calculated the electric dipole matrix elements (whose square is proportional to optical absorption), yielding analytical expressions as a function of chiral index and wavevector, k. As Ajiki and Ando, they found that parallel interband transitions are allowed only between massive bands of the same index and k-vector and not at all allowed between massless linear bands, for armchair species. Furthermore, by examining the kdependence of the matrix element, they found that the dipole matrix element reaches a maximum for k-values that coincide with the positions of the van Hove singularities (VHS) in the electronic density-of-states for each band.…”

Section: B Selection Rules For Optical Transitionsmentioning

confidence: 99%

Fundamental optical processes in armchair carbon nanotubes

Hároz

Duque

et al. 2013

Nanoscale

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Single-wall carbon nanotubes provide ideal model 1-D condensed matter systems in which to address fundamental questions in many-body physics, while, at the same time, they are leading candidates for building blocks in nanoscale optoelectronic circuits. Much attention has been recently paid to their optical properties, arising from 1-D excitons and phonons, which have been revealed via photoluminescence, Raman scattering, and ultrafast optical spectroscopy of semiconducting carbon nanotubes. On the contrary, dynamical properties of metallic nanotubes have been poorly explored, although they are expected to provide a novel setting for the study of electron-hole pairs in the presence of degenerate 1-D electrons. In particular, (n,n)-chirality, or armchair, metallic nanotubes are truly gapless with massless carriers, ideally suited for dynamical studies of Tomonaga-Luttinger liquids. Unfortunately, progress towards such studies has been slowed by the inherent problem of nanotube synthesis whereby both semiconducting and metallic nanotubes are produced. Here, we use post-synthesis separation methods based on density gradient ultracentrifugation and DNAbased ion-exchange chromatography to produce aqueous suspensions strongly enriched in armchair nanotubes. Through resonant Raman spectroscopy of the radial breathing mode phonons, we provide macroscopic and unambiguous evidence that density gradient ultracentrifugation can enrich armchair nanotubes. Furthermore, using conventional, optical absorption spectroscopy in the nearinfrared and visible range, we show that interband absorption in armchair nanotubes is strongly excitonic. Lastly, by examining the G-band mode in Raman spectra, we determine that observation of the broad, lower frequency (G − ) feature is a result of resonance with non-armchair "metallic" nanotubes. These findings regarding the fundamental optical absorption and scattering processes in metallic carbon nanotubes lay the foundation for further spectroscopic studies to probe many-body physical phenomena in one dimension.

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“…An exciton specified by a center-of-mass wave vector in the axis direction k c and u = (ζ,ξ,j ) where ζ and ξ denote the valleys for the electron and hole, respectively, and j is the index for the other degrees of freedom, is written by a superposition of electron-hole pair states as 2,12 …”

Section: Excitonsmentioning

confidence: 99%

“…[2][3][4][5][6][7][8][9][10][11] The optical response of the nanotubes is anisotropic where light polarized in parallel to the nanotube axis strongly excites excitons as compared to perpendicular polarization. 4,6,[12][13][14] For the excitons excited for the parallel polarization, electrons and holes are well associated with specific symmetric conduction and valence subbands with respect to the Fermi energy. Such excitons consisting of electrons and holes in the ith-lowest conduction and the ith-highest valence subbands, respectively, are denoted as E ii excitons.…”

Section: Introductionmentioning

confidence: 99%

Exciton scattering from impurities and acoustic phonons in carbon nanotubes

Fujimoto

Uryu

2013

Phys. Rev. B

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Exciton scattering from impurities and acoustic phonons in semiconducting carbon nanotubes is theoretically studied in an effective-mass approximation. A selection rule for transitions resulting from the scattering is obtained, showing that the ground-state exciton for the lowest-exciton band is never scattered from long-range impurities and deformation potentials near the band edge. This arises from the symmetry of nanotubes for the successive transformations of the charge conjugation and parity and for the reflection of the coordinate along the nanotube axis. Agreement of numerical results with recent experiments supports the validity of this selection rule.

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Exciton absorption of perpendicularly polarized light in carbon nanotubes

Cited by 91 publications

References 44 publications

Direct measurement of the absolute absorption spectrum of individual semiconducting single-wall carbon nanotubes

Direct measurement of the absolute absorption spectrum of individual semiconducting single-wall carbon nanotubes

Fundamental optical processes in armchair carbon nanotubes

Exciton scattering from impurities and acoustic phonons in carbon nanotubes

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