Three classes of one-dimensional, two-tile Penrose tilings and the Fibonacci Kronig-Penney model as a generic case
- 15 July 1988
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 38 (3) , 1709-1720
- https://doi.org/10.1103/physrevb.38.1709
Abstract
We generalize the Fibonacci Penrose tiling to three classes of one-dimensional, two-tile Penrose tilings which can be obtained geometrically as well as recursively. From a numerical study of their spectral properties, we conclude that the Fibonacci case has the generic features of all three classes. As a model of epitaxial quasiperiodic superlattices we consider a Fibonacci Kronig-Penney model and give a physical picture relating structural to spectral properties.Keywords
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