Spin-dependent polaron formation in pristine graphene

We investigate the effects of spin-orbit couplings on the electron (hole)-E-2g phonon interaction in graphene. We examine the effects of spin-orbit couplings on electron and hole polaron formation as well as DC conductivity, and spin polarizations of charge carriers. We use Frohlich type Hamiltonian to describe the electron-phonon system within the continuum limit. Our theoretical analysis shows that, the polaronic effect is decreased due to the spin-orbit couplings, for both spin and pseudospin states, but it is enhanced beyond some critical values of wavevector for spin-up states of both sublattices in the presence of spin-orbit couplings. The Rashba spin-orbit coupling in the graphene single layer splits up- and down- states, and produces perfect spin polarized conductivity. Also the phonon-restricted and phonon-assisted conduction are reported for positive and negative Fermi energies.