The effect of electron- phonon coupling in spin–orbit-coupled graphene

Abstract

We investigate the effects of electron- phonon and Rashba spin–orbit couplings on the electronic spectrum of pristine graphene charge carriers. We introduce a Fröhlich-type Hamiltonian describing the electron–phonon interaction in spin–orbit-coupled graphene, and propose a diagonalisation procedure to solve this Hamiltonian based on the Lee–Low–Pines theory which includes two successive unitary transformations. By means of these transformations, our results show that, in spin–orbit-coupled graphene, electron– phonon interaction lifts the degeneracy of two zero-gap branches and enhances the existing gap between other two branches. It is also found that the magnitude of the splitting in ungapped branches depends on the strength of spin–orbit interaction, and thus the emerging gap can be tuned by spin–orbit interaction.