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

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The electronic properties of one-dimensional graphene superlattices strongly depend on the atomic size and orientation of the 1D external periodic potential. Using a tight-binding approach, we show that the armchair and zigzag directions in these superlattices have a different impact on the renormalization of the anisotropic velocity of the charge carriers. For symmetric potential barriers, the velocity perpendicular to the barrier is modified for the armchair direction while remaining unchanged in the zigzag case. For asymmetric barriers, the initial symmetry between the forward and backward momentum with respect to the Dirac cone symmetry is broken for the velocity perpendicular (armchair case) or parallel (zigzag case) to the barriers. At last, Dirac cone multiplication at the charge neutrality point occurs only for the zigzag geometry. In contrast, band gaps appear in the electronic structure of the graphene superlattice with barrier in the armchair direction.