Effects of electron-acoustic phonon interaction in the presence of spin-orbit couplings in graphene

We investigate the effects of electron-zone center acoustic phonon interaction on spin-orbit couplings in pristine graphene. We examine the polaron formation and analyse the effects of spin-orbit couplings on polaron formation and electron-phonon couplings. Frohlich type Hamiltonian within the continuum limit is used to describe the electron-phonon system. With theoretical analysis, we show that, in the presence of electron-phonon interaction, the intrinsic and Rashba spin-orbit couplings of graphene become k dependent and Rashba spin-orbit coupling exhibits different characters with respect to spin orientation. Even there is a symmetry between electron-hole states if only one spin-orbit mechanism is present, electron-phonon coupling induces symmetry breaking between electron-hole states. Moreover, polaronic effect is decreased for both spin states, but it is increased beyond the some critical values of k for spin-up states in the presence of spin-orbit couplings. (C) 2015 Elsevier B.V. All rights reserved.