Symmetry-adapted tight-binding calculations of the totally symmetric A1 phonons of single-walled carbon nanotubes and their resonant Raman intensity

The atomistic calculations of the physical properties of perfect single-walled carbon nanotubes based on the use of the translational symmetry of the nanotubes face increasing computational difficulties for most of the presently synthesized nanotubes with up to a few thousand atoms in the unit cell. This difficulty can be circumvented by use of the helical symmetry of the nanotubes and a two-atom unit cell. We present the results of such symmetry-adapted tight-binding calculations of the totally symmetric A1 phonons (the RBM and the G-band modes) and their resonant Raman intensity for several hundred nanotubes.In particular, we show that (1) the frequencies and the resonant Raman intensity of the RBM and the G-band modes show diameter and chirality dependence and family patterns, (2) the strong electron–View the MathML source phonon interactions in metallic nanotubes lead to Kohn anomalies at the zone center, (3) the G-band consists of a subband due to View the MathML source phonons of semiconducting tubes centered at ∼1593 cm−1, a subband of View the MathML source phonons at ∼1570 cm−1, and a subband of View the MathML source phonons of metallic tubes at ∼1540 cm−1. The latter prediction confirms previous theoretical results but disagrees with the commonly adopted assignment of the G-band features.