Theory of elementary excitations in quasiperiodic structures

Abstract

The aim of this work is to present a comprehensive and up-to-date review of the main physical properties (such as energy profiles, localization, scale laws, multifractal analysis, transmission spectra, transmission fingerprints, electronic structures, magnetization curves and thermodynamic properties) of the elementary excitations that can propagate in multilayered structures with constituents arranged in a quasiperiodic fashion. These excitations include plasmon–polaritons, spin waves, light waves and electrons, among others. A complex fractal or multifractal profile of the energy spectra is the common feature among these excitations. The quasiperiodic property is formed by the incommensurate arrangement of periodic unit cells and can be of the type referred to as deterministic (or controlled) disorder. The resulting excitations are characterized by the nature of their Fourier spectrum, which can be dense pure point (as for the Fibonacci sequence) or singular continuous (as for the Thue-Morse and double-period sequences). These sequences are described in terms of a series of generations that obey particular recursion relations, and they can be considered as intermediate systems between a periodic crystal and the random amorphous solids, thus defining a novel description of disorder. A discussion is also included of some spectroscopic techniques used to probe the excitations, emphasizing Raman and Brillouin light scattering.