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.