▎ 摘　　要

In this paper, we report a first-principles study of the lattice dynamics of small graphene nanoribbon with zigzag edges. Our investigation is based on spin polarized density functional calculations (DFT). Nesting properties in the electronic band structure are very different for nanoribbons with unpolarized, ferromagnetic, and antiferromagnetic configurations. As a result, the phonon spectrum and nesting related softening in phonon frequencies differ in these cases. The unpolarized and ferromagnetic structures show nesting related phonon softening and considerable electron phonon linewidth, while for the antiferromagnetic structure, a band gap at the Fermi energy eliminates these effects. Saturating the nanoribbon edge with hydrogen has negligible effect on the phonon spectra for the magnetic structures while for the unpolarized configuration all structures without hydrogen are unstable due to soft phonon modes. The electron-phonon coupling coefficients have also been calculated and implications for Peierls transition and superconductivity are discussed.