Possible polaron formation of zigzag graphene nano-ribbon in the presence of Rashba spin–orbit coupling

•A tight binding study of Rashba spin–orbit coupling in a zigzag graphene nanoribbon is presented.•We show that even for small values of Rashba spin–orbit coupling the anti-ferromagnetic phase on the zigzag edges is disappeared.•Our results show the spin-dependent polaron formation energy in zigzag nanoribbon.

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.

Graphical abstractWe study the effect of Rashba spin–orbit coupling and the electron–phonon interaction on the electronic structure of zigzag graphene nanoribbon.Figure optionsDownload full-size imageDownload as PowerPoint slide