Binding energy and lifetime of excitons in metallic nanotubes

The difficulty of describing excitons in semiconducting SWNTs analytically lies with the fact that excitons can neither be considered strictly 1D nor 2D objects. However, the situation changes in the case of metallic nanotubes where, by virtue of screening from gapless metallic subbands, the radius of the exciton becomes much larger than the radius of the nanotube R_ex » R. We develop the theory of excitons in metallic nanotubes, determine their binding energy and show that it represents about 0.1 of the band gap, in agreement with the existing experimental data. Additionally, because of the presence of the gapless subbands, there are processes where bound excitons are scattered into unbound electron-hole pairs belonging to the gapless subbands. Such processes lead to a finite exciton lifetime and the broadening of its spectral function. We calculate the corresponding decay rate of the excitons.