▎ 摘　　要

We study graphene nanoribbons (GNRs) with armchair edges in the presence of Rashba spin-orbit interactions (RSOI). We impose the boundary conditions on the tight binding Hamiltonians for bulk graphene with RSOI by means of a sine transform and study the influence of RSOI on the spectra and the spin polarization in detail. We derive the low energy approximation of the RSOI Hamiltonian for the zeroth and first order in momentum and test their ranges of validity. The choice of a basis appropriate for armchair boundaries is important in the case of mode-coupling effects and leads to results that are easy to work with.