Can fractal-like spectra be experimentally observed in aperiodic superlattices?

Abstract

We numerically investigate the effects of inhomogeneities in the energy spectrum of aperiodic semiconductor superlattices, focusing our attention on Thue-Morse and Fibonacci sequences. In the absence of disorder, the corresponding electronic spectra are self-similar. The presence of certain degree of randomness, due to imperfections occurring during the growth processes, gives rise to a progressive loss of quantum coherence, smearing out the finer details of the energy spectra predicted for perfect aperiodic superlattices and spurring the onset of electron localization. However, depending on the degree of disorder introduced, a critical size for the system exists, below which peculiar transport properties, related to the pre-fractal nature of the energy spectrum, may be measured.

Nature of the eigenstates in the miniband of random dimer-barrier superlattices

“…Let us take a system constructed with two kinds of blocks distributed randomly on a lattice. It is evident that the effects of randomness will be removed when, for a given electron energy, the positions of two consecutive different blocks can be interchanged [39]. In this case all the blocks of each type can be moved to one of the two sides.…”

Selective spatial localization of the atom displacements in one-dimensional hybrid quasi-regular (Thue–Morse and Rudin–Shapiro)/periodic structures

“…These structures do not appear in the nature, but can be produced in the laboratory as multilayer systems [4][5][6][7] by molecular beam epitaxy (MBE) techniques. The interest on these systems was increased after the predictions that they would exhibit peculiar electron and phonon critical states and highly fragmented fractal energy spectra [8][9][10][11][12][13][14][15]. Many works have been devoted to the study of the basic properties of quasiregular structures, as it can be seen in [16,17].…”

“…The vibrational spectrum of quasi-regular structures presents a highly fragmented character [12,15,27]. By using different materials as the starting ones we can have different realizations (ABAAB.…”

Vibrational properties of quasiregular systems with mirror symmetry

“…Quasiregular structures have generated a lot of interest as derived of the prediction that these systems would exhibit peculiar electron and phonon critical states and highly fragmented fractal energy spectra [1][2][3][4][5][6][7][8]. Some realizations of this kind of systems have been obtained in the laboratory as multilayer structures [9][10][11][12].…”