Fibonacci invariant and electronic properties of GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As quasiperiodic superlattices

A theoretical study of the electronic properties of GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Al}}_{\mathrm{x}}$As quasiperiodic Fibonacci superlattices reveals the striking differences to be expected in the band structure, wave-function localization, and optical transitions of superlattices having quasiperiodic modulation either in the barrier width or in the barrier height. We show how these differences are related to the value of the Fibonacci invariant. The results of photoluminescence excitation spectroscopy experiments are also presented.