Binding Energy and Lifetime of Excitons in Metallic Nanotubes

Due to the large screening of Coulomb interaction between electrons in higher dimensions in metallic materials, a bound state of electron-hole pair cannot be formed. However, in lower dimensional materials such as carbon nanotubes due to less effective screening of electrons allows the formation of bound state of electron-hole pair whose radius, R_ex » R. This is particularly unique to metallic nanotubes in a sense that the problem of describing excitons can now be considered 1D as compared to semiconducting nanotubes where exciton radius R_ex ∼ R and excitons are neither 1D nor 2D. We are thus able to determine the binding energy of excitons in metallic nanotubes, is about 0.08 v/R. 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.