Optical Properties Of Carbon Nanotubes Research Articles

Effect of Exciton-Phonon Coupling in the Calculated Optical Absorption of Carbon Nanotubes

We find that the optical properties of carbon nanotubes reflect remarkably strong effects of exciton-phonon coupling. Tight-binding calculations show that a significant fraction of the spectral weight of the absorption peak is transferred to a distinct exciton+phonon sideband, which is peaked at around 200 meV above the main absorption peak. This sideband provides a distinctive signature of the excitonic character of the optical transition. The exciton-phonon coupling is reflected in a dynamical structural distortion, which contributes a binding energy of up to 100 meV. The distortion is surprisingly long ranged, and is strongly dependent on chirality.

Linear and nonlinear optical properties of carbon nanotubes from first-principles calculations

A systematic ab initio study of the optical as well as structural and electronic properties of the carbon nanotubes within density-functional theory in the local-density approximation has been performed. Highly accurate full-potential projected augmented wave method was used. Specifically, the optical dielectric function $\ensuremath{\varepsilon}$ and second-order optical susceptibility ${\ensuremath{\chi}}^{(2)}$ as well as the band structure of a number of the armchair [(3,3),(5,5),(10,10),(15,15),(20,20)], zigzag [(5,0),(10,0),(15,0),(20,0)] and chiral [(4,2),(6,2),(6,4),(8,4), (10,5)] carbon nanotubes have been calculated. The underlying atomic structure of the carbon nanotubes was determined theoretically. It is found that for the electric field parallel to the nanotube axis $(E\ensuremath{\Vert}\mathrm{z\ifmmode \hat{}\else \^{}\fi{}}),$ the absorptive part ${\ensuremath{\varepsilon}}^{\ensuremath{''}}$ of the optical dielectric function for the small nanotubes (the diameter being smaller than, say, 25 \AA{}) in the low-energy range (0--8 eV) consists of a few distinct peaks. Furthermore, the energy position, the shape, and the number of the peaks depend rather strongly on the diameter and chirality. This suggests that one could use these distinct optical features to characterize the chirality and diameter of the grown nanotubes. In contrast, for the electric field perpendicular to the nanotube axis $(E\ensuremath{\perp}\mathrm{z\ifmmode \hat{}\else \^{}\fi{}}),$ the ${\ensuremath{\varepsilon}}^{\ensuremath{''}}$ spectrum of all the nanotubes studied except the three 4 \AA{} nanotubes in the low-energy region is made up of a broad hump. The bandwidth of the hump increases with the nanotube diameter and the magnitude of the hump is in general about half of that of the ${\ensuremath{\varepsilon}}^{\ensuremath{''}}$ for $E\ensuremath{\Vert}\mathrm{z\ifmmode \hat{}\else \^{}\fi{}}.$ Surprisingly, given their one-dimensional character, the optical anisotropy of the nanotubes is smaller than that of graphite. For the nanotubes with a moderate diameter (say, 30 \AA{}) such as the (20,20) nanotube, the optical anisotropy is not large and the ${\ensuremath{\varepsilon}}^{\ensuremath{''}}$ spectrum for both electric-field polarizations becomes rather similar to that of graphite with electric-field parallel to the graphene layers $(E\ensuremath{\perp}c).$ The calculated static polarizability $\ensuremath{\alpha}(0)$ for the semiconducting nanotubes is rather anisotropic with $\ensuremath{\alpha}(0)$ for $E\ensuremath{\Vert}\mathrm{z\ifmmode \hat{}\else \^{}\fi{}}$ being several times larger than that for $E\ensuremath{\perp}\mathrm{z\ifmmode \hat{}\else \^{}\fi{}}.$ For both electric-field polarizations, $\ensuremath{\alpha}(0)$ is nearly proportional to the square of the tube diameter. The calculated electron energy loss spectra of all the nanotubes studied here for both electric field polarizations are similar to that of $E\ensuremath{\perp}c$ of graphite, being dominated by a broad $(\ensuremath{\pi}+\ensuremath{\sigma})$-electron plasmon peak at near 27 eV and a small $\ensuremath{\pi}$-electron plasmon peak at 5--7 eV. Only the chiral nanotubes would exhibit second-order nonlinear optical behavior. Furthermore, only two tensor elements ${\ensuremath{\chi}}_{\mathrm{xyz}}^{(2)}$ and ${\ensuremath{\chi}}_{\mathrm{yzx}}^{(2)}$ are possibly nonzero with ${\ensuremath{\chi}}_{\mathrm{xyz}}^{(2)}=\ensuremath{-}{\ensuremath{\chi}}_{\mathrm{yzx}}^{(2)}.$ For all the chiral nanotubes studied here, both the real and imaginary parts of ${\ensuremath{\chi}}_{\mathrm{xyz}}^{(2)}(\ensuremath{-}2\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega})$ show an oscillatory behavior. The absolute value of ${\ensuremath{\chi}}_{\mathrm{xyz}}^{(2)}(\ensuremath{-}2\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega})$ of all the chiral nanotubes in the photon energy range of 0.1--3.0 eV is huge, being up to ten times larger than that of GaAs, suggesting that chiral nanotubes have potential applications in nonlinear optics, e.g., second-harmonic generation and sum-frequency generation. Nevertheless, the static value of both ${\ensuremath{\chi}}_{\mathrm{xyz}}^{(2)}$ and ${\ensuremath{\chi}}_{\mathrm{yzx}}^{(2)}$ is zero.

Electronic and photonic properties of doped carbon nanotubes.

The idea of doping carbon nanotubes is attractive since it provides various possibilities for controlling the physical properties of carbon nanotubes. In this review, we have summarized recent progress on the experimental and theoretical studies of carbon nanotubes doped with nonmetals, alkali metals, transition metals, and clusters. The doping effects on the electronic, magnetic, transport, and optical properties of carbon nanotubes are reviewed. The related applications of carbon nanotubes in nanoelectronics, battery, field emission, spintronics, nonlinear optics, and chemical sensors are discussed.

Variational approach to excitons in carbon nanotubes

Excitons in quasi-one-dimensional semiconductors may lower the optical transition energies by a substantial amount. To quantify the effect in carbon nanotubes, we apply a simple variational approach. In excitonic units, apower law with exponent ∼-0.6 is obtained for the binding energy dependence on nanotube radius. When converted to ordinary units, the ratio of binding energy to tight-binding band gap yields a roughly constant value of nearly 40%. This substantial ratio implies that exciton effects are of prime importance for the optical properties of carbon nanotubes.

Magnetoelectronic and optical properties of carbon nanotubes

Magnetoelectronic and optical properties of carbon nanotubes are, respectively, studied within the ${\mathrm{sp}}^{3}$ tight-binding model and the gradient approximation. They strongly depend on the magnitude and the direction of the magnetic field, the nanotube geometry (radius and chiral angle), and the Zeeman splitting. The magnetic field would lead to the change of energy gap, the destruction of state degeneracy, and the coupling of different angular momenta. Hence there are magnetic-field-dependent absorption frequencies and more absorption peaks. The types of carbon nanotubes predominate in the band structure and thus the range of absorption frequencies and the number of absorption peaks. The Zeeman splitting makes the semiconductor-metal transition occur at lower magnetic flux. It metalizes armchair carbon nanotubes in the presence of the perpendicular magnetic field. However, it does not affect the optical excitations except for metallic carbon nanotubes.

π-band contribution to the optical properties of carbon nanotubes: Effects of chirality

We study the \ensuremath{\pi}-band contribution to the optical properties of the carbon nanotubes based on the tight-binding model, including optical absorptions, optical rotatory power, and circular dichroism. By taking into account not only the interband contributions but also the free-carrier contributions, the dielectric functions and the third-rank tensor responsible for the optical activity are calculated. The following have been shown. (i) The features of the dielectric functions are consistent with the ellipsometry experiments by de Heer and co-workers [Science 268, 845 (1995)]; (ii) The calculated plasma frequency is of the same order of magnitude as the one recently observed by Bommeli et al. [Solid State Commun. 99, 513 (1996)]. (iii) Chiral nanotubes are, as expected, optically active and the spectra of their optical rotatory power (RP) and circular dichroism (CD) are highly oscillatory. (iv) Nanotubes with a diameter about 4 nm can give RP and CD that are of the same order of magnitude as those of certain organic compounds. (v) The RP and CD decrease as the diameter increases.

Evidence of anisotropic metallic behaviour in the optical properties of carbon nanotubes

We have conducted reflectivity measurements on carbon nanotubes from the far-infrared up to the ultraviolet, in order to achieve the complete excitation spectrum. We have analysed our experimental findings in terms of the Maxwell-Garnett (MG) effective medium model, where small conducting particles are dispersed in a dielectric host-medium. The fair agreement between our experimental data and the phenomenological MG-approach suggests that carbon nanotubes have an intrinsic and anisotropic metallic behaviour.

Plasmons and optical properties of carbon nanotubes.

The optical properties of carbon nanotubes are studied within the gradient approximation. The calculated dielectric function exhibits many divergent structures, due to the divergencies in its density of states. As a result, the electron-energy-loss spectrum has many peak structures, including a prominent one at \ensuremath{\sim}6 eV, which is identified as the collective excitations of the \ensuremath{\pi}-band electrons. This plasmon is found to be insensitive to both radius and chiral angle, due to the unique one-dimensional band structure of carbon nanotubes. The result is consistent with the experimental measurements. The reflectance also exhibits many interesting features, including a weak but sharp plasmon edge at \ensuremath{\sim}6 eV.