Rashba spin-orbit coupling effects in armchair graphene nanoribbons

We study the influence of the Rashba spin-orbit coupling effects on the electronic properties of armchair graphene nanoribbons (GNRs). By utilizing both analytical and numerical schemes, we show that the finite width of the graphene nanoribbon breaks its energy spectrum into an infinite number of bands. By considering the Rashba spin-orbit coupling term as a perturbation, we show that zero energy bands between electron and hole states at Dirac points are lifted into a finite bandgap.