Tyshchenko S. Band structure and interband transitions in carbon nanotubes

Based on the method of zero-range potentials, a solvable model with a single universal fitting parameter has been developed to obtain the wave functions and the dispersion equations for the band pi-electrons in arbitrary single- walled carbon nonotubes and graphite plane, their geometrical structures being completely taken into account. The spatial structure of nanotubes was modeled in the form of a certain number of identical monoatomic spirals shifted one with respect to another. Such an approach significantly simplifies the calculations for chiral nanotubes with more than a thousand atoms in the elementary cell and leads to two dispersion equations describing the extended zone scheme. The wave functions and dispersion equations obtained were used to investigate the absorption spectrum of polarized light caused by direct interband transitions in isolated nanotubes. The selection rules were obtained. It was shown that, at least, within the above approximation, the circular dichroism is absent in chiral nanotubes for a light wave propagating along the tube axis. The results obtained are in a good accordance with existing experimental data.