Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2012-04-17
European Physical Journal B, Vol. 84, No. 4, 2011, pp. 415-421
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
7 pages, 3 figures
Scientific paper
10.1140/epjb/e2011-20323-7
From the quantum mechanical point of view, the electronic characteristics of quasicrystals are determined by the nature of their eigenstates. A practicable way to obtain information about the properties of these wave functions is studying the scaling behavior of the generalized inverse participation numbers $Z_q \sim N^{-D_q(q-1)}$ with the system size $N$. In particular, we investigate $d$-dimensional quasiperiodic models based on different metallic-mean quasiperiodic sequences. We obtain the eigenstates of the one-dimensional metallic-mean chains by numerical calculations for a tight-binding model. Higher dimensional solutions of the associated generalized labyrinth tiling are then constructed by a product approach from the one-dimensional solutions. Numerical results suggest that the relation $D_q^{d\mathrm{d}} = d D_q^\mathrm{1d}$ holds for these models. Using the product structure of the labyrinth tiling we prove that this relation is always satisfied for the silver-mean model and that the scaling exponents approach this relation for large system sizes also for the other metallic-mean systems.
Schreiber Michael
Thiem Stefanie
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