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

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) over bar). Furthermore, the zero-(k) over bar 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. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4729133]