Exciton-phonon sidebands in metallic carbon nanotubes studied using semiconductor Bloch equations

We use semiconductor Bloch equations to describe excitonic absorption spectra of metallic carbon nanotubes. In particular, we focus on the formation of exciton-phonon induced sidebands. Our approach is based on the density matrix formalism combining zone-folded tight-binding wave functions and electron-phonon coupling, allowing a straight-forward description of temporal and spectral many-body interactions. We observe clear excitonic features in the spectra of metallic carbon nanotubes in agreement with recent experimental and theoretical studies. Furthermore, depending on the temperature, we find significant exciton-phonon sidebands on both sides of the zero-phonon excitonic line. We investigate the polaronic shift and the transfer of the spectral weight to the sidebands for a variety of metallic nanotubes with different chiral angles and diameters.