Abstract
The electronic properties of a tight-binding model which possesses two types of hopping matrix element (or on-site energy) arranged in a Fibonacci sequence are studied. The wave functions are either self-similar (fractal) or chaotic and show ‘‘critical’’ (or ‘‘exotic’’) behavior. Scaling analysis for the self-similar wave functions at the center of the band and also at the edge of the band is performed. The energy spectrum is a Cantor set with zero Lebesque measure. The density of states is singularly concentrated with an index which takes a value in the range [,]. The fractal dimensions f() of these singularities in the Cantor set are calculated. This function f() represents the global scaling properties of the Cantor-set spectrum.
- Received 31 July 1986
DOI:https://doi.org/10.1103/PhysRevB.35.1020
©1987 American Physical Society