Exotic electronic properties in Thue-Morse graphene superlattices.

To show the specific behavior of Dirac fermions in a quasi-periodic structure, we investigate the electronic properties in a deterministic Thue-Morse graphene superlattice. Our main findings include the following. (i) Unlike conventional Schrödinger electrons, quasi-periodic features such as the striking self-similarity and trifurcation in the transmission spectrum can be manifested only at oblique incidence. (ii) In the vicinity of the usual Dirac point, extra Dirac points emerge; their locations are dependent merely on the second generation of the Thue-Morse structure and the number is double that in the periodic graphene superlattice. (iii) A classification is given about the wavefunctions in the Thue-Morse structure which are transformed from the critical states into extended ones at the Dirac points. (iv) The electrons can transmit perfectly at the extra Dirac points, and such a collimation supplies a convenient way to experimentally detect the numbers and the locations of the extra Dirac points. These exotic electronic properties in the aperiodic graphene superlattices may facilitate some applications in graphene-based electronics.