Less singular quasicrystals: The case of low codimensions - art. no. 140201

We consider a set of tilings proposed recently as d-dimensional generalizat ions of the Fibonacci chain, by Vidal and Mosseri. These tilings have a par ticularly simple theoretical description, making them appealing candidates for analytical solutions for electronic properties. Given their self-simila r geometry, one could expect that the tight-binding spectra of these tiling s might possess the characteristically singular features of well-known quas iperiodic systems such as the Penrose or the octagonal tilings. We show her e, by a numerical study of statistical properties of the tight-binding spec tra that these tilings fall rather in an intermediate category between the crystal and the quasicrystal, i.e., in a class of almost integrable models. This is certainly a consequence of the low codimension of the tilings.