States of Excitons and Linear Optical Spectra in Metallic Single-Walled Carbon Nanotubes

Considering the exciton effect, the excitation energy and its binding energy of the metallic single-walled carbon nanotubes (SWNTs) are theoretically studied by using the simple tight-binding model, based on which the linear absorption spectra are also calculated. It is found that due to the trigonal warping effect, the excitation energies of the linear optical spectra all are split into two corresponding ones. Additionally, the splitting depends on both the chirality and the transition energy: (1) the splitting is maximal for the zigzag tubes, the splitting decreases with the increasing chiral angle; (2) the higher the transition energy is, the larger the splitting is. It is very interesting to find that the obtained results are in good agreement with the experimental results.