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

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We have studied the electronic properties in aperiodic graphene superlattices of Thue-Morse sequence. Although the structure is aperiodic, an unusual Dirac point (DP) does exist and its location is exactly at the energy corresponding to the zero-averaged wave number (zero-k¯). Furthermore, the zero-k¯ gap associated with the DP is robust against the lattice constants and the incident angles, and multi-DPs may appear under the suitable conditions. A resultant controllability of electronic transport in Thue-Morse sequence is predicted, which may facilitate the development of many graphene-based electronics.