Ab-initio study of the effects induced by the electron-phonon scattering in carbon based nanostructures

In this paper we investigate from first principles the effect of the electron-phonon interaction in two paradigmatic nanostructures: trans-polyacetylene and polyethylene. We found that the strong electron-phonon interaction leads to the appearance of complex structures in the frequency dependent electronic self-energy. Those structures rule out any quasi-particle picture, and make the adiabatic and static approximations commonly used in the well-established Heine Allen Cardona (HAC) approach inadequate. We propose, instead, a fully ab-initio dynamical formulation of the problem within the Many Body Perturbation Theory framework. The present dynamical theory reveals that the structures appearing in the electronic self-energy are connected to the existence of packets of correlated electron/phonon states. These states appear in the spectral functions even at $T=0\,K$, revealing the key role played by the zero point motion effect. We give a physical interpretation of these states by disclosing their internal composition by mapping the Many Body problem to the solution of an eigenvalue problem.