Abstract: We investigate the effects of coupling to multiple-phonon modes on the properties of a Holstein polaron. To this end, we generalize the Momentum Average approximations MA((0)) and MA((1)) to deal with multiple-phonon modes. As for a single-phonon mode, these approximations are found to be numerically very efficient. They become exact for very weak or very strong couplings, and are highly accurate in the intermediate regimes, e.g. the spectral weights obey exactly the first six, respectively eight, sum rules. Our results show that the effect on ground-state properties is cumulative in nature. As a result, if the effective coupling to one mode is much larger than to all the others, this mode effectively determines the ground-state properties. However, even very weak coupling to a second phonon mode has important non-perturbational effects on the higher-energy spectrum, in particular on the dispersion and the phonon statistics of the polaron band. This has important consequences on the analysis and interpretation of data for real materials.

Abstract: The changes induced by exposing multi-walled carbon nanotubes (CNTs) to atomic nitrogen were analysed by high-resolution transmission electron microscopy (HRTEM), x-ray and ultraviolet photoelectron spectroscopy. It was found that the atomic nitrogen generated by a microwave plasma effectively grafts chemical groups onto the CNT surface altering the density of valence electronic states. HRTEM showed that the exposure to atomic nitrogen does not significantly damage the CNT surface.