Rashba spin-orbit interaction in graphene and zigzag nanoribbons

We investigate the effects of Rashba spin-orbit (RSO) interactions on the electronic band structure and corresponding wave functions of graphene. By exactly solving a tight-binding model Hamiltonian we obtain the expected splitting of the bands—due to the SU(2) spin symmetry breaking—that is accompanied by the appearance of additional Dirac points. These points are originated by valence-conduction-band crossings. By introducing a convenient gauge transformation we study a model for zigzag nanoribbons with RSO interactions. We show that RSO interactions lift the quasidegeneracy of the edge band while introducing a state-dependent spin separation in real space. Calculation of the average magnetization perpendicular to the ribbon plane suggest that RSO could be used to produce spin-polarized currents. Comparisons with the intrinsic spin-orbit interaction proposed to exist in graphene are also presented.