One-dimensional Disorder Research Articles

Structure, microstructure and disorder in low temperature chemical vapor deposited SiC coatings

Chemical vapor deposited SiC coatings were investigated at different scales by X-Ray diffraction, Raman microspectroscopy and transmission electron microscopy. They were prepared under specific conditions explaining the various (micro)structures obtained. The deposits all have a columnar morphology with a preferential orientation and a faulted cubic structure. They differ in how disorder is incorporated in the structure. Fine XRD analyses and stacking fault density assessment by TEM revealed the one-dimensionally-disordered (ODD) polytype in the <111> textured coatings. The frequency and spatial distribution of stacking faults vary and sometimes locally generate periodic alpha sequences. A specific type of disorder was also identified where {111} planes are arranged parallel to the growth direction within the columns. These disorders, more energetic than stacking faults, induce multiple and particularly large Raman modes. Crystal distortions, such as dislocations, are localized at the ODD domain boundaries, which are frequently interrupted as they extend during the growth.

Role of the second nearest-neighbor hoppings in a disordered Bose–Hubbard Hamiltonian in the Many-Body Localization

We investigate in this work the survival of the Many-Body Localization in a discrete disordered Bose–Hubbard Hamiltonian when the second nearest-neighbor hoppings are taken into account. We consider small size systems of cold atoms located in a one-dimensional disorder optical lattices. Considering the disorder strength, we focus our attention on the spectral properties of the quantum many-body system such as the level-spacing statistics. As a result, the shapes of the probability distributions show that the systems undergo a delocalized and a localized regimes for low and high disorder strength respectively. This result is reinforced by the mean-square deviation studies.

Strong structural occupation ratio effect on mechanical properties of silicon carbide nanowires

Materials’ mechanical properties highly depend on their internal structures. Designing novel structure is an effective route to improve materials’ performance. One-dimensional disordered (ODD) structure is a kind of particular structure in silicon carbide (SiC), which highly affects its mechanical properties. Herein, we show that SiC nanowires (NWs) containing ODD structure (with an occupation ratio of 32.6%) exhibit ultrahigh tensile strength and elastic strain, which are up to 13.7 GPa and 12% respectively, approaching the ideal theoretical limit. The ODD structural occupation ratio effect on mechanical properties of SiC NWs has been systematically studied and a saddle shaped tendency for the strength versus occupation ratio is firstly revealed. The strength increases with the increase of the ODD occupation ratio but decreases when the occupation ratio exceeds a critical value of ~ 32.6%, micro twins appear in the ODD region when the ODD segment increases and soften the ODD segment, finally results in a decrease of the strength.

A smeared quantum phase transition in disordered holography

We study the effects of quenched one-dimensional disorder on the holographic Weyl semimetal quantum phase transition (QPT), with a particular focus on the quantum critical region. We observe the smearing of the sharp QPT linked to the appearance of rare regions at the horizon where locally the order parameter is non-zero. We discuss the role of the disorder correlation and we compare our results to expectations from condensed matter theory at weak coupling. We analyze also the interplay of finite temperature and disorder. Within the quantum critical region we find indications for the presence of log-oscillatory structures in the order parameter hinting at the existence of an IR fixed point with discrete scale invariance.

Novel modification of anhydrous transition metal oxalates from powder diffraction.

The known metal-C2O4 structures may be divided into two modifications, α and β. The α-modification has an order-disorder struxture, revealing one-dimensional disordering of the metal-oxalate chains, and the β-modification is ordered. The crystal structures of orthorhombic γ-MnC2O4 {poly[μ-oxalato-manganese(II)]; space group Pmna, a = 7.1333 (1), b = 5.8787 (1), c = 9.0186 (2) Å, V = 378.19 (1) Å3, Z = 4 and Dx = 2.511 Mg m-3} and γ-CdC2O4 {poly[μ-oxalato-cadmium(II)]; space group Pmna, a = 7.3218 (1), b = 6.0231 (1), c = 9.2546 (2) Å, V = 408.13 (1) Å3, Z = 4 and Dx = 3.262 Mg m-3} have been obtained from powder diffraction patterns. The structures are isostructural. Each metal atom in each structure is coordinated by seven O atoms which belong to five oxalate ions. The crystal packing, which contains noticeable cavities in the [101] and [001] directions, is not close packed and essentially differs from the known disordered α- and ordered β-modifications of transition metal oxalates. This modification seems to be metastable. It was found that a spontaneous γ→β phase transition takes place for γ-CdC2O4.

Nanostructures in silicon carbide crystals and films

Phase transformations of SiC crystals with grown original defects and thin films have been presented. The SiC crystals were grown by the Tairov method and the films were obtained by the “sandwich” and Chemical Vapor Deposition (CVD) methods.The analysis of absorption spectra, excitation spectra and low-temperature photoluminescence spectra testifies to the formation of a new microphase during the growth. The complex spectrum can be decomposed into similar structure-constituting spectra shifted on the energy scale relative to the former. Such spectra are indicators of the formation of new nanophases.The joint consideration of photoluminescence spectra, excitement photoluminescence spectra and absorption spectra testifies to the uniformity of different spectra and the autonomy of each of them. Structurally, the total complexity spectra correlate with the degree of disorder (imperfection) of the crystal and are related to the peculiarities of a defective performance such as a one-dimensional disorder. Three different types of spectra have three different principles of construction and behavior.

Universal role of quantum uncertainty in Anderson metal–insulator transition

We explore quantum uncertainty, based on Wigner–Yanase skew information, in various one-dimensional single-electron wave functions. For the power-law function and eigenfunctions in the Aubry–André model, the electronic localization properties are well-defined. For them, we find that quantum uncertainty is relatively small and large for delocalized and localized states, respectively. And around the transition points, the first-order derivative of the quantum uncertainty exhibits singular behavior. All these characters can be used as signatures of the transition from a delocalized phase to a localized one. With this criterion, we also study the quantum uncertainty in one-dimensional disorder system with long-range correlated potential. The results show that the first-order derivative of spectrum-averaged quantum uncertainty is minimal at a certain correlation exponent αm for a finite system, and has perfect finite-size scaling behaviors around αm. By extrapolating αm, the threshold value αc≃1.56±0.02 is obtained for the infinite system. Thus we give another perspective and propose a consistent interpretation for the discrepancies about localization property in the long-range correlated potential model. These results suggest that the quantum uncertainty can provide us with a new physical intuition to the localization transition in these models.

Electron supercollimation in graphene and Dirac fermion materials using one-dimensional disorder potentials.

Electron supercollimation, in which a wave packet is guided to move undistorted along a selected direction, is a highly desirable property that has yet to be realized experimentally. Disorder in general is expected to inhibit supercollimation. Here we report a counterintuitive phenomenon of electron supercollimation by disorder in graphene and related Dirac fermion materials. We show that one can use one-dimensional disorder potentials to control electron wave packet transport. This is distinct from known systems where an electron wave packet would be further spread by disorder and hindered in the potential fluctuating direction. The predicted phenomenon has significant implications in the understanding and applications of electron transport in Dirac fermion materials.

New triclinic modification of lead iodate Pb(IO3)2: Synthesis and crystal structure

A new triclinic modification of lead iodate Pb(IO3)2 (space group \(C\bar 1\)) is obtained under hydrothermal conditions. The crystal structure is determined without preliminary knowledge of the chemical formula. [IO3]− groups, which are characteristic of pentavalent iodine, have a typical umbrella-like configuration. The new phase has a more complex structure than the known orthorhombic modification. The arrangement of heavy Pb and I atoms follows a’ = a/3 pseudoperiodicity. In the layers of two types that form sheets parallel to the ab plane, Pb and I atoms have different coordinations. A polytypic nature of the new modification is responsible for the one-dimensional disordering along the a axis as well as different variants of layer alternation. It is possible to obtain crystals of acentric and polar derivatives of the centrosymmetric phase that will be promising for application.

Dc electric field effect on the anomalous exponent of the hopping conduction in the one-dimensional disorder model

The dc electric field effect on the anomalous exponent of the hopping conduction in the disorder model is investigated. First, we explain the model and derive an analytical expression of the effective waiting time for the general case. We show that the exponent depends on the external field. Then we focus on a one-dimensional system in order to illustrate the features of the anomalous exponent. We derive approximate expressions of the anomalous exponent of the system analytically. For the case of a weak field, the anomalous exponent is consistent with that of diffusive systems. This is consistent with the treatments of Barkai et al. [Phys. Rev. E 63, 046118 (2001)] and our result supports their theory. On the other hand, for the case of a strong field and a strong disorder, the time evolution of the exponent clearly differs from that in the weak field. The exponent is consistent with the well-known expression of the anomalous exponent in the multiple trapping model at mesoscopic time scales. In the long-time limit, a transition of the anomalous exponent to the same value of the weak field occurs. These findings are verified by the Monte Carlo simulation.

X-ray scattering on one-dimensional disordered structures

The review shows different treatments and methods for the analysis of the X-ray diffraction patterns from the crystals disordered in one direction; the possibilities, limitations, and applications of each method are discussed. The author also provides the examples of simulation of the diffraction patterns for the crystals, which have the effects on the experimental X-ray patterns related with 1D disordering. Several structural types and different kinds of one-dimensional disorder are considered.

IS THE REGIME WITH SHOT NOISE SUPPRESSION BY A FACTOR 1/3 ACHIEVABLE IN SEMICONDUCTOR DEVICES WITH MESOSCOPIC DIMENSIONS?

We discuss the possibility of diffusive conduction and thus of suppression of shot noise by a factor 1/3 in mesoscopic semiconductor devices with two-dimensional and one-dimensional potential disorder, for which existing experimental data do not provide a conclusive result. On the basis of our numerical analysis, we conclude that it is quite difficult to achieve diffusive transport over a reasonably wide parameter range, unless the device dimensions are increased up to the macroscopic scale where, however, shot noise disappears because the device length exceeds the Debye length. In addition, in the case of one-dimensional disorder, some mechanism capable of mode-mixing has to be present in order to reach or even approach the diffusive regime.

Local atomic order in sodiump-chlorobenzenesulfonate monohydrate studied by pair distribution function analyses and lattice-energy minimisations

Routine X-ray single-crystal structure analysis of Na[C6H4ClO3S]·H2O resulted in an orthorhombic layer structure with space group Pnma, Z=4. In this crystal structure the phenyl rings in a single layer are disordered over two mutually perpendicular orientations with occupancies of 0.500(4) each. Structure determination including superstructure reflections and irregular shaped reflections revealed a twinned, ordered, monoclinic structure, P21/c, Z=8. Here, within a layer the phenyl rings are arranged alternatingly perpendicular. Pair distribution function analysis (PDF) and lattice-energy calculations confirmed this arrangement. Faint diffuse scattering streaks point to a one-dimensional disorder (concerning the layer-stacking sequence). Application of the order-disorder (OD) approach led to three polytype structures with maximum degree of order (MDO); one of them is the experimental monoclinic structure. This structure was found to have the most favourable energy in the lattice-energy minimisations. However, the energy differences between different polytypes with different stacking sequences are rather small. Hence, the lattice-energy minimisations confirmed the monoclinic P21/c structure with stacking disorder.

X-ray diffraction from nonperiodic layered structures with correlations: analytical calculation and experiment on mixed Aurivillius films

X-ray diffraction from films consisting of layers with different thicknesses, structures and chemical contents is analysed. The disorder is described by probabilities for different sequences of layers. Closed analytical expressions for the diffracted X-ray intensity are obtained when the layers form a stationary Markov chain. The proposed model is applied to the diffraction data from epitaxial sodium bismuth titanate thin films with Aurivillius structure possessing such one-dimensional disorder. In this case, the disorder is caused by a random stacking of three and four perovskite units separated by bismuth oxide interlayers. The results of analytical calculations are in good agreement with the experimental data and indicate that the incorporation of sodium in the Bi(4)Ti(3)O(12) phase causes the formation of a fourth perovskite unit.

Brownmillerites as members of the unified OD family with two-dimensional disorder: A topology and symmetry analysis, the prediction of structures, and the properties of crystals

A topology and symmetry analysis of the structures of the brownmillerite family is performed within the OD theory. Blocks of two types with two-dimensional periodicity (“layers”) are revealed in two main structural types with Ibm2 and Pcmn symmetry. The high local symmetry of one layer is not characteristic of the other layer or of the structure as a whole. This feature determines the possibility of varying the arrangement of pairs of layers and the existence of one-dimensional disorder, as well as of structures with a maximum degree of order, periodic structures, and disordered structures. A symmetry analysis allows one to reveal the second direction of disordering (two-dimensional disorder), which is comparatively uncommon. The structure law of the family, which allows the systematic predicting of commensurate structural models without applying the fourth dimension, is described. Structure-property relationships are considered.

Tunable disorder in a crystal of cold polar molecules

We show that a two-species mixture of polar molecules trapped on an optical lattice gives rise to a system of rotational excitons in the presence of tunable impurities. The exciton-impurity interactions can be controlled by an external electric field, which can be exploited for quantum simulation of localization phenomena in disordered media. We demonstrate that an external electric field can be used to induce resonant enhancement of the exciton-impurity scattering cross sections and delocalization of excitonic states in a correlated one-dimensional disorder potential.

The local structure and composition of Ba 4Nb 2O 9-based oxycarbonates

X-ray powder-diffraction (XRD), high-resolution transmission electron microscopy (HRTEM), electron diffraction (ED), infrared spectroscopy (IR), thermogravimetry (TG) and mass spectroscopy (MS) were performed to investigate the composition and the crystal structure of tetra-barium di-niobate (V) Ba 4Nb 2O 9. The TG, MS and IR studies revealed that the compound is a hydrated oxycarbonate. Assuming that the carbonate stoichiometrically replaces oxygen, the composition of the low-temperature α-modification, obtained by slow cooling from 1100 °C, corresponds to Ba 4Nb 2O 8.8(CO 3) 0.2·0.1H 2O, while the quenched high-temperature γ-modification has the Ba 4Nb 2O 8.42(CO 3) 0.58·0.38H 2O composition. The α-phase has a composite incommensurately modulated structure consisting of two mutually interacting [Ba] ∞ and the [(Nb,□)O 3] ∞ subsystems. The composite modulated crystal structure of the α-phase can be described with the lattice parameters a=10.2688(1) Å, c=2.82426(8) Å, q=0.66774(2) c* and a superspace group R 3 ¯ m(00γ)0 s. The HRTEM analysis demonstrates the nanoscale twinning of the trigonal domains parallel to the {1 0 0} crystallographic planes. The twinning introduces a one-dimensional disorder into the [(Nb,□)O 3] ∞ subsystem, which results in an average P 6 ¯ 2 c crystal structure of the α-phase. Possible places for the carbonate group in the structure are discussed using a comparison with other hexagonal perovskite-based oxycarbonates.

Effects of Atom-Atom Interaction on Localization and Adiabaticity of BEC in One-Dimensional Disorder Optical Lattice

We numerically simulate the dynamical behavior of BEC in one-dimensional incommensurable optical lattice by split-step Fourier method in a time-dependent one-dimensional Gross—Pitaevskii equation. It is indicated that the atom-atom interaction will weaken the localization and broaden the wave function, and it will destroy the adiabaticity of the ramped loading process in both single lattice and incommensurate lattice due to the broadening effect. A band structure model can interpret the difference of the adiabatic condition with non-interacting BEC in these optical lattices.

Stoichiometry and Bravais lattice diversity: Anab initiostudy of the GaSb(001) surface

We study the family of GaSb(001)-$(4\ifmmode\times\else\texttimes\fi{}3)$ reconstructions by ab initio density-functional theory. For each possible surface stoichiometry between the well-known Sb-poor $\ensuremath{\alpha}(4\ifmmode\times\else\texttimes\fi{}3)$ and Sb-rich $\ensuremath{\beta}(4\ifmmode\times\else\texttimes\fi{}3)$ phases, we find thermodynamically stable reconstructions. Surface energies of $(4\ifmmode\times\else\texttimes\fi{}3)$ unit cells shifted relative to each other are computed for the thermodynamically stable phases. Especially, the energetic costs for unit-cell shifts along the $[\overline{1}10]$ direction with the length of one in-plane surface lattice constant are very low. In a comparative study, we show that this is similar to the $\ensuremath{\beta}2(2\ifmmode\times\else\texttimes\fi{}4)$ reconstructed GaAs(001) surface with a one-dimensional disorder along $[\overline{1}10]$, but different from the $c(4\ifmmode\times\else\texttimes\fi{}4)$ reconstruction. The diversity in surface stoichiometry and unit-cell shape allows us to explain the contradicting experimental results obtained by scanning tunneling microscopy and surface-diffraction techniques at finite substrate temperatures.

Lyapunov exponent for the laser speckle potential: A weak disorder expansion

Anderson localization of matter waves was recently observed with cold atoms in a weak one-dimensional disorder realized with laser speckle potential [Billy et al., Nature (London) 453, 891 (2008)]. The latter is special in that it does not have spatial frequency components above certain cutoff ${q}_{c}$. As a result, the Lyapunov exponent (LE) or inverse localization length vanishes in Born approximation for particle wave vector $kg\frac{1}{2}{q}_{c}$, and higher orders become essential. These terms, up to the fourth order, are calculated analytically and compared with numerical simulations. For very weak disorder, LE exhibits a sharp drop at $k=\frac{1}{2}{q}_{c}$. For moderate disorder (a) the drop is less dramatic than expected from the fourth-order approximation and (b) LE becomes very sensitive to the sign of the disorder skewness (which can be controlled in cold atom experiments). Both observations are related to the strongly non-Gaussian character of the speckle intensity.