▎ 摘　　要

In this article we study the role of Rashba spin-orbit coupling and electron-phonon interaction on the electronic structure of zigzag graphene nanoribbon with different width. The total Hamiltonian of nanoribbon is written in the tight binding form and the electron-electron interaction is modeled in the Hubbard term. We used a unitary transformation to reach an effective Hamiltonian for nano ribbon in the presence of electron-phonon interaction. Our results show that small Rashba spin orbit coupling annihilates the anti-ferromagnetic phase in the zigzag edges of ribbon and the electron-phonon interaction yields small polaron formation in graphene nano ribbon. Furthermore, Rashba type spin-orbit coupling increases (decreases) the polaron formation energy for up (down) spin state. (C) 2014 Elsevier B.V. All rights reserved.