Abstract
After the discovery of quasicrystals exhibiting fivefold symmetry and thus a lack of periodic long range order(1), a good deal of work has been performed to understand the crystallography of such structures and the nature of their elementary excitations. The main results are that the Fourier transform of the quasilattice (which generalizes the notion of periodic reciprocal space) is made of a dense but countable (d.c.) set of delta functions(2,3), and that the allowed energies for excitations span a Cantor set(4,5). The simplest models were developped for the paradigmic one dimensional (1D) quasicrystal: the Fibonacci superlattice.
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Paquet, D., Joncour, M.C., Jusserand, B., Laruelle, F., Mollot, F., Etienne, B. (1989). Structural and Optical Properties of Periodic Fibonacci Superlattices. In: Fasol, G., Fasolino, A., Lugli, P. (eds) Spectroscopy of Semiconductor Microstructures. NATO ASI Series, vol 206. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6565-6_14
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