Double-periodic quasi-periodic graphene superlattice: non-Bragg band gap and electronic transport

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Electronic band gap and transport in quasi-periodic graphene superlattice of double-periodic sequence have been investigated. It is found that such quasi-periodic structure can possess a zero-averaged wave number (zero-k) gap which associated with an unusual Dirac point. Different from Bragg gap, the zero-k gap is less sensitive to the incidence angle, and robust against the lattice constants. The locations of Dirac point and multi-Dirac-points in the graphene superlattices of various sequences are also compared. The control of electron transport over the zero-k band gap in graphene superlattice may facilitate the development of many graphene-based electronics.