We study graphene nanoribbons (GNRs) with armchair edges in the presence ofRashba spin-orbit interaction (RSOI). We impose the boundary conditions on thetight binding Hamiltonians for bulk graphene with RSOI by means of a sinetransform and study in detail the influence of RSOI on the spectra and the spinpolarization. We show that the spin polarization perpendicular to the GNRchanges sign when reversing the momentum along the GNR if the bands are coupledby strong RSOI. Furthermore, we derive a linearized approximation to the RSOIHamiltonian and find that only the neighboring modes of an energy band have tobe taken into account in order to achieve a good approximation for the sameband. Due to their experimental availability and various proposals forengineering appropriate RSOI, GNRs with armchair edges are a promisingcandidate for possible spintronics applications.
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