Abstract
The electronic spectrum of one-dimensional quasiperiodic materialssuch as AB1-xCx (0≤ x≤ 1) is calculated hereinwithin the framework of the off-diagonal tight-binding model by using asimple scheme of the theory of the binary quasiperiodic lattices.The spectrum shows a Cantor-set of energy bands and consists of a centerband gap for the whole range of x.We find that unless the potential difference is too strong, the magnitude of the center band gap Δx is interpolated by aVegard's law type linear relation with respect to x asΔx=(1-x)Δab+xΔac, where Δab (Δac)is the band gap for the regular AB (AC) alloy.This means that this system is a semiconductor for0≤ x≤ 1.We also show that the center gap follows the Saxon-Hutner-Luttinger theorem.
