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

TL;DR

This paper numerically explores how inhomogeneities affect the self-similar energy spectra of aperiodic superlattices, revealing conditions under which fractal-like spectral features can be experimentally observed despite disorder.

Contribution

It demonstrates the impact of disorder on aperiodic superlattices' spectra and identifies a critical size for observing fractal spectral features.

Findings

Disorder causes smearing of spectral details and electron localization.

A critical system size exists below which fractal spectral properties can be observed.

Transport properties are influenced by the pre-fractal nature of the energy spectrum.

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.