In this paper, the electronic band structures and its transport properties in the gapped graphene superlattices, with one-dimensional (1D) periodic potentials of square barriers, are systematically investigated. It is found that a zero averaged wave-number (zero-$overline{k}$ ) gap is formed inside the gapped graphene-based superlattices, and the condition for obtaining such a zero-$overline{k}$ gap is analytically presented. The properties of this zero-$overline{k}$ gap including its transmission, conductance and Fano factor are studied in detail. Finally it is revealed that the properties of the electronic transmission, conductance and Fano factor near the zero-$overline{k}$ gap are very insensitive to the structural disorder for the finite graphene-based periodic-barrier systems.
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