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The electronic properties of one-dimensional graphene superlattices stronglydepend on the atomic size and orientation of the 1D external periodicpotential. Using a tight-binding approach, we show that the armchair and zigzagdirections in these superlattices have a different impact on therenormalization of the anisotropic velocity of the charge carriers. Forsymmetric potential barriers, the velocity perpendicular to the barrier ismodified for the armchair direction while remaining unchanged in the zigzagcase. For asymmetric barriers, the initial symmetry between the forward andbackward momentum with respect to the Dirac cone symmetry is broken for thevelocity perpendicular (armchair case) or parallel (zigzag case) to thebarriers. At last, Dirac cone multiplication at the charge neutrality pointoccurs only for the zigzag geometry. In contrast, band gaps appear in theelectronic structure of the graphene superlattice with barrier in the armchairdirection.

Velocity renormalization and Dirac cone multiplication in graphene superlattices with various barrier edge geometries