Coexistence of localized, critical, and extended states in a one-dimensional substitutional non-Fibonaccian quasicrystal: A multifractal analysis

We have studied the electronic properties of a new tight-binding model with two on-site energies arranged in a non-Fibonaccian quasicrystalline sequence. The wave functions are numerically determined and are either localized, critical, or extended. A multifractal analysis of the wave functions is performed, and it is shown that nonlocalized states belonging to the part of the spectrum with zero Lebesque measure are characterized by multifractal behavior to all length scales, whereas extended states exhibit a fractal-nonfractal crossover at a critical length ${\xi }_c$.