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We study the effects of the structural corrugation or rippling on theelectronic properties of undoped armchair graphene nanoribbons (AGNR). First,reanalyzing the single corrugated graphene layer we find that the twoinequivalent Dirac points (DP), move away one from the other. Otherwise, theFermi velocity decrease by increasing rippling. Regarding the AGNRs, whosemetallic behavior depends on their width, we analyze in particular the case ofthe zero gap band-structure AGNRs. By solving the Dirac equation with theadequate boundary condition we show that due to the shifting of the DP a gapopens in the spectra. This gap scale with the square of the rate between thehigh and the wavelength of the deformation. We confirm this prediction by exactnumerical solution of the finite width rippled AGNR. Moreover, we find that thequantum conductance, calculated by the non equilibrium Green's functiontechnique vanish when the gap open. The main conclusion of our results is thata conductance gap should appear for all undoped corrugated AGNR independent oftheir width.

Spectral gap induced by structural corrugation in armchair graphene nanoribbons