Optical and Loss Spectra of Carbon Nanotubes: Depolarization Effects and Intertube Interactions

Abstract

We performed ab initio calculations of the anisotropic dielectric response of small-diameter single-walled carbon nanotubes in the framework of time-dependent density-functional theory. The calculated optical spectra are in very good agreement with experiment, both concerning absolute peak positions and anisotropy effects. The latter can only be described correctly when crystal local-field effects ("depolarization" effects) are fully taken into account. Moreover, interactions between the tubes can strongly modify their absorption and electron energy-loss spectra.

Ab initiostudy of the dielectric response of crystalline ropes of metallic single-walled carbon nanotubes: Tube-diameter and helicity effects

“…The calculations were based on the random-phase approximation ͑RPA͒ with inclusion of the crystal local-field effects ͑LFEs͒ in the response for the cases that this is necessary. This approximation was found sufficient in an earlier study of the optical absorption of small-diameter carbon tubes 19 predicting absorption-peak positions in very good agreement with experiment 25 and more elaborate calculations 15 that considered excitonic effects. Furthermore, our EELS calculations in graphite matched very well the experimentally observed spectra and plasmon-peak positions.…”

“…Recent theoretical calculations of the optical-absorption spectra for these tubes showed that the position of the ab-sorption peaks is very sensitive to tube helicity. 15,18,19 In contrast, the energy-loss function in the range of the + plasmon and in the vanishing-q limit did not exhibit a helicity dependence. 19,20 Here, however, we provide a more complete assessment of the effect of different helicities by making the comparisons in an extended range of q.…”

“…15,18,19 In contrast, the energy-loss function in the range of the + plasmon and in the vanishing-q limit did not exhibit a helicity dependence. 19,20 Here, however, we provide a more complete assessment of the effect of different helicities by making the comparisons in an extended range of q. This represents a more realistic situation since the experimental EELS data are always obtained for finite momentum transfer q.…”

“…The direction of q is always along the tube axis. For this polarization, it was shown 19 that the peak positions in the optical-absorption spectra are not affected by the intertube interaction, allowing therefore comparison of the present results with Raman experiments 4 on isolated nanotubes. It is also important to note here that for more general q orientations, the dielectric response will be modified; recent calculations 20 of the EELS spectra for the ͑3,3͒ tubes showed that for q components perpendicular to the tubes axis the spectra became more diffuse with increasingly more important LFE that leads to a shift of the plasmon peaks to higher frequencies.…”

“…These calculations were done for a large variety of chiral and nonchiral nanotubes of various diameters and helped to elucidate aspects of the response in a frequency range up to 15 eV, where → Ã excitations dominate. ͑c͒ First-principles calculations based on either many-body perturbation theory [15][16][17] or density-functional [18][19][20][21][22] and Hartree-Fock 23,24 time-dependent frameworks using different approximations for exchangecorrelation effects. Unfortunately, such calculations are still restricted to nanotubes of very small diameters ͑around 4 Å in most cases͒ and to the lower part of the valence-electron excitation spectrum.…”