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. (paper)