A multifractal analysis of optical phonon excitations in quasicrystals

It is shown that the allowed frequencies of optical phonon modes propagating in quasiperiodic AlN–GaN structures display a multifractal behavior. This feature is confirmed through a scaling-exponent analysis of a parametric spectrum of singularities f(α). This is done by using an alternative counting method, avoiding the use of a Legendre transform, which could lead to distortions. The Cantor-like spectrum is also investigated, and scaling properties are shown for Fibonacci, Thue–Morse and double-period quasiperiodic superlattices.