One-dimensional Fibonacci-class quasilattices are proposed and studied, which are constructed by the substitution rules B→B nϪ1 A, A→B nϪ1 AB. We have proved that this class of binary lattices is self-similar and also quasiperiodic. By the use of the renormalization-group technique, it has been proved that for all Fibonacciclass lattices the electronic energy spectra are perfect self-similar, and the branching rules of spectra are obtained. We analytically prove that each energy gap can be simply labeled by a characteristic integer, i.e., for the Fibonacci-class lattices there is a universal gap-labeling theorem ͓Phys. Rev. B 46, 9216 ͑1992͔͒.
The density of electron states, p(E), in disordered systems in the band-tail region near band edges is investigated. %'e show that the p(E) of the Halperin and Lax type derived by Sa-yakanit predicts, in three dimensions, an exponential (Urbach) band tail for the correlation lengths found in amorphous Si and within the energy range observed in optical absorption near band edges. The simple exponential behavior is not universal and may not, for example, be observed in heavily doped semiconductors.
The "band-tail" density of states p(E) available to electrons in a field of randomly distributed, attractive impurities developed in previous work is extended to higher energy E. Numerical values of p(E) are also presented (1) for comparison with p(E) developed by other methods and (2) for calculation of optical and other properties of heavily doped semicoflductors depending on p(E).
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