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

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.

Figure 1

Calculated RPA absorption spectra with (continuous lines) and without (dashed lines) LFE. For the (3,3) tubes, results for both the isolated ones (thin lines) and in the solid (thick lines) are presented. For comparison, the JDOS are also shown (upper panel). The TDLDA result for the (3,3) isolated tubes is given in the second panel (dotted line). The results for the (5,0) and (4,2) tubes are only shown for the parallel polarization where LFE are negligible. The spectra for the perpendicular polarization have been multiplied by 2. The experimental data [6] are shown in the inset for parallel (solid line) and perpendicular polarization (dotted line).

Figure 2

Calculated RPA loss function for the (3,3) distant tubes (thin line) and solid (thick line) of tubes without LFE. $\mathbf{q}$ is parallel to the tube axis. Dashed curves are the results for graphite (thick) and graphene (thin) for in-layer $\mathbf{q}$ [16].