Optical Absorption Spectra in Finite Double-Walled Carbon Nanotubes

The tight-binding model and the modified gradient approximation are, respectively, used to calculate the electronic states and optical properties of finite double-walled carbon nanotubes (DWCNTs). The optical absorption spectra allow us to decompose the total DWCNT spectral function into the contributions from the inner and outer walls. Intertube interactions can cause drastic changes in the symmetry of the electronic states, the Fermi level, the energy spacing, and the state degeneracy. Such effects are directly reflected in the joint density of states and optical absorption spectra. Thus, the first absorption peaks of the energy degeneracy (nondegeneracy) of two finite single-walled carbon nanotubes would be separated into three or four peaks in the shorter DWCNTs. For finite armchair DWCNTs, the number of the first group peaks decreases as the length increases. These results demonstrate a competition between the tube length, the intertube interactions, and the geometric structures. For finite zigzag DWCNTs however, the number of the first group peaks remains constant as the length increases. This phenomenon can be attributed to the states exclusively localized at the outermost zigzag positions. The energies of the peaks make a red-shift as the tube length increases. For sufficiently long DWCNTs absorption peak energies are almost independent of length.