Spectral gap induced by structural corrugation in armchair graphene nanoribbons

We study the effects of the structural corrugation or rippling on the electronic properties of undoped armchair graphene nanoribbons (AGNRs). First, reanalyzing the single corrugated graphene layer we find that the two inequivalent Dirac points (DPs) move away from each other. Futhermore, the Fermi velocity v(F) decreases when the rippling increases. Regarding the AGNRs, whose metallic behavior depends on their widths, we analyze, in particular, the case of the zero-gap band-structure AGNRs. By solving the Dirac equation with adequate boundary conditions we show that, due to the shifting of the DP, a gap opens up in the spectra. This gap scales with the square of the rate between the height and the wavelength of the deformation. We confirm this prediction by an exact numerical solution of the finite width rippled AGNR. Moreover, we find that the quantum conductance, calculated by the nonequilibrium Green's function technique, vanishes when the gap opens up. The main conclusion of our results is that a conductance gap should appear for all undoped corrugated AGNR, independently of their widths.