We investigate electronic band structure and transport properties in bilayer graphene superlattices of Thue-Morse sequence. It is interesting to find that the zero-$bar{k}$ gap center is sensitive to interlayer coupling $t$, and the centers of all gaps shift versus $t$ at a linear way. Extra Dirac points may emerge at $k_{y} e$0, and when the extra Dirac points are generated in pairs, the electronic conductance obeys a diffusive law, and the Fano factor tends to be 1/3 as the order of Thue-Morse sequence increases. Our results provide a flexible and effective way to control the transport properties in graphene.
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