Electronic band gaps and transport in aperiodic graphene-based superlattices of Thue-Morse sequence

We investigate electronic band structure and transport properties in aperiodic graphene-based superlattices of Thue-Morse (TM) sequence. The robust properties of zero-$\overline{k}$ gap are demonstrated in both mono-layer and bi-layer graphene TM sequence. The Extra Dirac points may emerge at $k_{y}\ne$0, and the electronic transport behaviors such as the conductance and the Fano factor are discussed in detail. Our results provide a flexible and effective way to control the transport properties in graphene-based superlattices.