Raman Scattering from Phonons in Quasiperiodic Superlattices Based on Generalizations of the Fibonacci Sequence

Abstract

Recently there has been a great deal of interest in the structural, vibrational, and electronic properties of nonperiodic superlattices.¹ This work has been stimulated by the discovery of quasicrystals² and the realization that 1-D analogs of quasicrystals could be created artificially in multilayer systems.³ By far the majority of the work in these systems has concentrated on quasiperiodic Fibonacci superlattices.⁴ The Fibonacci structure is a particular case of a class of quasiperiodic structures defined by the recursion relation⁵

$$ {{S}_{j}} = {{({{S}_{{j - 1}}})}^{n}}{{S}_{{j - 2}}} $$

((1))

By defining the basic building blocks S₁ and S₂ in terms of layers of different materials and thicknesses we have attached a basis to the quasiperiodic lattice. Table 1 illustrates how the recursion relation (1) is used to build up the first 5 generations in terms of S₁ and S₂.