Electronic spectrum of a two-dimensional Fibonacci lattice

The electronic spectrum and wave functions of a new quasicrystal structure- a two-dimensional Fibonacci lattice-are investigated in the tight-binding a pproximation using the method of the level statistics. This is a self-simil ar structure consisting of three elementary structural units. The "central" and "nodal" decoration of this structure are examined. It is shown that th e electronic energy spectrum of a two-dimensional Fibonacci lattice contain s a singular part, but in contrast to a one-dimensional Fibonacci lattice t he spectrum does not contain a hierarchical gap structure. The measure of a llowed states (Lebesgue measure) of the spectrum is different from zero, an d for "central" decoration it is close to 1. The character of the localizat ion of the wave functions is investigated, and it is found that the wave fu nctions are "critical." (C) 1999 American Institute of Physics. [S1063-7761 (99)02411-7].