Xiujun Fu

Relationship between Penrose vertices and decagonal covering configurations

Two-dimensional quasicrystals are generally described by the Penrose tiling model. An alternative is the cluster covering approach developed recently. There exists a correspondence between the two schemes. The distributions of rhombus vertices in Penrose tilings and the nearest neighbor configurations in the decagonal covering structures are studied. Their occurrence probabilities are expressed in terms of the powers of the golden mean τ and their relationship is obtained.

Configuration correlations in decagonal covering structures

Quasiperiodic structures can be generated by cluster covering approach. In a decagonal covering pattern there are nine nearest neighbor configurations. These basic configurations exhibit certain correlations in the whole system and will develop to higher order configurations, which reflect the local structures concerning the neighbors beyond the nearest ones.

LOCALIZED ELECTRONIC STATES IN A TERNARY QUASIPERIODIC MODEL

The one-dimensional ternary sequence generated by the substitutions S --> M, M --> L, L --> LS is generally called SML quasiperiodic model [Phys. Rev. B43, 13240 (1991)], the electronic localization of which is studied. For this model, the Fourier transform, the band-width dependence on site number, the second moment and multifractal behaviors of wavefunctions are investigated. It is found that the lattice structure is quasiperiodic, but the energy spectrum is of pure point and the electronic states are all localized, which exhibits the characteristic of disordered systems.

STRUCTURE OF MOBILITY EDGES IN A ONE-DIMENSIONAL INCOMMENSURATE MODEL

The localization of the Soukoulis-Economou model in one-dimensional incommensurate systems is studied by the use pf multifractal analysis. In the case of epsilon(n) = 1.9[cos(2 pi omega n)+ 1/3cos(4 pi omega n)] and omega = lim(l) (-->) (infinity) F-l-1/F-l where F-l is the generalized Fibonacci number satisfying the recursion relation F-l = 8F(l-1)+ F-l-1 with F-0 = F-1 = 1, we have numerically found a hierarchical and selfsimilar structure of mobility edges. The results suggest the existence of an infinite number of mobility edges.

GAP-LABELING PROPERTIES OF THE ENERGY SPECTRUM FOR TWO-DIMENSIONAL FIBONACCI QUASILATTICES

We have analytically obtained the occupation probabilities on subbands of the hierarchical energy spectrum and the step heights of the integrated density of states for two-dimensional Fibonacci quasilattices. Based on the above results, the gap-labeling properties of the energy spectrum are found, which claim that the step height is equal to {mτ}, where the braces denote the fractional part, and m is an integer that can be used to label the corresponding energy gap. Numerical results confirm these results very well.