Aperiodic Disorder Research Articles

Graphene-embedded planar and cylindrical Oldenburger–Kolakoski aperiodic photonic crystals

In this paper, we examine the transmission and absorption spectra of light waves in both planar and cylindrical quasiperiodic structures known as Photonic Crystals. In these quasiperiodic multilayers, graphene sheets are inserted between planar and concentric layers of two different dielectric materials (namely TiO2 and SiO2). These structures are called Planar Photonic Crystals (PPCs) and Cylindrical Photonic Crystals (CPCs), respectively. The spatial arrangement of the dielectric layers follows the aperiodic Oldenburger–Kolakoski (O–K) sequence. The transfer matrix method is used to calculate the transmission and absorption spectra of obliquely incident TE and TM waves to investigate the effects of graphene, aperiodic disorder, and incidence angle on the physical behavior of the system. The numerical results reveal that the transmission spectra for cylindrical geometry differ significantly from those for planar geometry, even in the case of a normal incidence angle. Furthermore, the transmission of TM modes is higher than that of TE modes for incidence angles greater than 30°. Finally, we have demonstrated that a substantial number of peaks in the absorption spectra for the CPC case are higher than those for the PPC case, which is a result that may be useful for enhancing the efficiency of optical sensors.

Localization for the Ising Model in a Transverse Field with Generic Aperiodic Disorder

We show that the transverse field Ising model undergoes a zero temperature phase transition for a Gδ set of ergodic transverse fields. We apply our results to the special case of quasiperiodic transverse fields, in one dimension we find a sharp condition for the existence of a phase transition.

Finite current stationary states of random walks on one-dimensional lattices with aperiodic disorder

Stationary states of random walks with finite induced drift velocity on one-dimensional lattices with aperiodic disorder are investigated by scaling analysis. Three aperiodic sequences, the Thue-Morse (TM), the paperfolding (PF), and the Rudin-Shapiro (RS) sequences, are used to construct the aperiodic disorder. These are binary sequences, composed of two symbols A and B, and the ratio of the number of As to that of Bs converges to unity in the infinite sequence length limit, but their effects on diffusional behavior are different. For the TM model, the stationary distribution is extended, as in the case without current, and the drift velocity is independent of the system size. For the PF model and the RS model, as the system size increases, the hierarchical and fractal structure and the localized structure, respectively, are broken by a finite current and changed to an extended distribution if the system size becomes larger than a certain threshold value. Correspondingly, the drift velocity is saturated in a large system while in a small system it decreases as the system size increases.

Neutron Diffraction and X-ray Absorption Fine Structure Evidence for Local Lattice Distortions and Aperiodic Antisite Substitution in Cu2ZnSnS4 Nanoparticles

A thorough structure determination has been performed on Cu2ZnSnS4 nanoparticles, a popular photovoltaic material, using neutron diffraction—to characterize the long-range average crystal structure—and X-ray absorption fine structure (XAFS) spectroscopy at the Cu, Zn, and Sn K-edges to elucidate the element-specific local structure. This is the first combined multiscale approach on nanoparticles of this material. The results indicate the presence of aperiodic disorder on the cation sites that is diminished by annealing. This disorder involves local lattice distortions around the crystallographic sites rather than the presence of interstitial atoms. It is most consistent with the known antisite substitutions that are integral to CZTS (referring to the ordering of the Cu, Zn, and Sn between planes). However, instead of being confined within single unit cells so as to maintain the crystallographic symmetry, periodicity, and homogeneity, the substitutional disorder appears to extend over larger regions consis...

Scaling analysis of stationary probability distributions of random walks on one-dimensional lattices with aperiodic disorder.

Stationary probability distributions of one-dimensional random walks on lattices with aperiodic disorder are investigated. The pattern of the distribution is closely related to the diffusional behavior, which depends on the wandering exponent Ω of the background aperiodic sequence: If Ω<0, the diffusion is normal and the distribution is extended. If Ω>0, the diffusion is ultraslow and the distribution is localized. If Ω=0, the diffusion is anomalous and the distribution is singular, which shows its complex and hierarchical structure. Multifractal analyses are performed in order to characterize these distributions. Extended, localized, and singular distributions are clearly distinguished only by the finite-size scaling behavior of α_{min} and f(α_{min}). The multifractal spectrum of the singular distribution agrees well with that of a simple partitioning process.

Renormalization of two-dimensional Ising systems with irrelevant, marginal and relevant aperiodic (dis)order

We introduce a class of 2d Ising models with aperiodic modulations of the coupling constants following a 2d substitution rule. The relevance of the aperiodicity to the phase transition is examined through an approximative real space renormalization group approach known as the cumulant approximation. We find that the relevance of the aperiodic disorder is determined by the fluctuations of the mean coupling as predicted by the Harris–Luck criterion.

Surface properties of aperiodic Ising quantum chains

We consider Ising quantum chains with quenched aperiodic disorder of the coupling constants given through general substitution rules. The critical scaling behaviour of several bulk and surface quantities is obtained by exact real space renormalization.

Aperiodic Ising quantum chains

Some years ago, Luck proposed a relevance criterion for the effect of aperiodic disorder on the critical behaviour of ferromagnetic Ising systems. In this article, we show how Luck's criterion can be derived within an exact renormalization scheme for Ising quantum chains with coupling constants modulated according to substitution rules. Luck's conjectures for this case are confirmed and refined. Among other outcomes, we give an exact formula for the correlation length critical exponent for arbitrary two-letter substitution sequences with marginal fluctuations of the coupling constants.