Theory of Optical Processes in Single-Walled Carbon Nanotubes

Carbon nanotubes exhibit a variety of unique electrical, mechanical, magnetic, and optical properties that make them attractive for potential applications in nanotechnology. In this project the energy band structure of single-walled carbon nanotubes of arbitrary chirality is computed using a tight binding scheme that is generalized to include second nearest neighbor interactions. Plots of this band structure and the corresponding energy density of states may be used to predict the conduction properties of nanotubes, including the band-gaps of those exhibiting semiconductor behaviors, and the effective mass of electrons near the band edge. They may also be used to predict the energies of allowed optical transitions for incident light polarized along the tube axis as well as relative probability of observing each. Plots of the Brillouin zones in the reciprocal lattice give a qualitative explanation of the energy band structure. Finally, the model is modified to include the effect of a magnetic field parallel to the tube axis, which splits degenerate energy levels and narrows the band-gap between the valence and conduction bands. The amounts of splitting and band-gap reduction are dependent on the Aharonov-Bohm flux passing through the tube.