Gap states and localization properties of one-dimensional Fibonacci quasicrystals

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Abstract
Localization lengths of electronic states on one-dimensional Fibonacci quasicrystals are calculated exactly within a decimation-renormalization scheme. A self-similar pattern is obtained for the localization lengths along the spectrum as the numerical resolution is improved. Properties of the states in the spectrum are inferred from the scaling of the gap states as the gap width approaches zero. No exponential localization is present for any type of model (diagonal and/or off-diagonal quasiperiodicity). Power-law-type localization has also been investigated and not found, at least in a standard form.