Uncorrelated Disorder Research Articles

Synchronization in Coupled Laser Arrays with Correlated and Uncorrelated Disorder.

The effect of quenched disorder in a many-body system is experimentally investigated in a controlled fashion. It is done by measuring the phase synchronization (i.e., mutual coherence) of 400 coupled lasers as a function of tunable disorder and coupling strengths. The results reveal that correlated disorder has a nontrivial effect on the decrease of phase synchronization, which depends on the ratio of the disorder correlation length over the average number of synchronized lasers. The experimental results are supported by numerical simulations and analytic derivations.

Nonuniversal critical dynamics on planar random lattices with heterogeneous degree distributions

The weighted planar stochastic (WPS) lattice introduces a topological disorder that emerges from a multifractal structure. Its dual network has a power-law degree distribution and is embedded in a two-dimensional space, forming a planar network. We modify the original recipe to construct WPS networks with degree distributions interpolating smoothly between the original power-law tail, P(q)∼q−α with exponent α≈5.6, and a square lattice. We analyze the role of the disorder in the modified WPS model, considering the critical behavior of the contact process (CP). We report a critical scaling depending on the network degree distribution. The scaling exponents differ from the standard mean-field behavior reported for CP on infinite-dimensional (random) graphs with power-law degree distribution. Furthermore, the disorder present in the WPS lattice model is in agreement with the Luck-Harris criterion for the relevance of disorder in critical dynamics. However, despite the same wandering exponent ω=1/2, the disorder effects observed for the WPS lattice are weaker than those found for uncorrelated disorder.

Quantum engineering for compactly localized states in disordered Lieb lattices

Blending ordering within an uncorrelated disorder potential in families of 3D Lieb lattices preserves the macroscopic degeneracy of compact localized states and yields unconventional combinations of localized and delocalized phases—as shown in Liu et al. (Phys Rev B 106:214204, 2022). We proceed to reintroduce translation invariance in the system by further ordering the disorder, and discuss the spectral structure and eigenstates features of the resulting perturbed lattices. We restore order in steps by first (i) rendering the disorder binary—i.e., yielding a randomized checkerboard potential, then (ii) reordering the randomized checkerboard into an ordered one, and at last (iii) realigning all the checkerboard values yielding a constant potential shift, but only on a sub-lattice. Along this path, we test the influence of additional random impurities on the order restoration. We find that in each of these steps, about half of the dispersive states are projected upon the unperturbed sites hosting the degenerate compact states, while the remaining ones are localized in the perturbed sites with energy determined by the strength of checkerboard. This strategy, herewith implemented in the 3D Lieb lattice, highlights order restoration as experimental pathway to engineer spectral and states features in disordered lattice structures in the pursuit of quantum storage and memory applications.Graphic abstract

Bias-induced circular current in a loop nanojunction with AAH modulation: Role of hopping dimerization

In this work, we investigate the interplay between correlated disorder and hopping dimerization on bias-driven circular current in a loop conductor that is clamped between two electrodes. The correlated disorder is introduced in site energies of the ring in the form of Aubry-André-Harper (AAH) model. Simulating the quantum system within a tight-binding framework all the results are worked out based on the waveguide theory. Unlike transport current, circular current in the loop conductor can get enhanced with increasing disorder strength. This enhancement becomes much effective when hopping dimerization is included which is taken following the Su-Schrieffer-Heeger (SSH) model. The characteristic features of bias-driven circular current are studied under different input conditions and we find that the results are robust for a wide range of physical parameters. For the sake of completeness, uncorrelated disorder is also considered. Our analysis may provide a new insight in analyzing transport behavior in different disordered lattices in the presence of additional restrictions in hopping integrals.

Floquet topological phase transitions induced by uncorrelated or correlated disorder

Floquet topological phase transitions induced by uncorrelated or correlated disorder

Imperfect phononic crystals work too: The effect of translational and mid-plane symmetry breaking on hypersound propagation

Translationally symmetric nanostructures, termed phononic crystals (PnCs), offer control over the propagation of acoustic phonons in the gigahertz (GHz) range for signal-processing applications and thermal management at sub-Kelvin temperatures. In this work, we utilize Brillouin light scattering to investigate the impact of symmetry breaking on GHz phonon propagation in PnCs made of holey silicon nanomembranes. We show that the lattice of thimble-like holes leads to broken mid-plane symmetry and, hence, to anticrossing acoustic band gaps. With the rising level of uncorrelated translational disorder, the phononic effects are gradually suppressed, starting at higher frequencies. Strikingly, the low-frequency partial Bragg bandgap remains robust up to the highest level of disorder.

High-throughput speckle spectrometers based on multifractal scattering media

We present compact integrated speckle spectrometers based on monofractal and multifractal scattering media in a silicon-on-insulator platform. Through both numerical and experimental studies we demonstrate enhanced optical throughput, and hence signal-to-noise ratio, for a number of random structures with tailored multifractal geometries without affecting the spectral decay of the speckle correlation functions. Moreover, we show that the developed multifractal media outperform traditional scattering spectrometers based on uniform random distributions of scattering centers. Our findings establish the potential of low-density random media with multifractal correlations for integrated on-chip applications beyond what is possible with uncorrelated random disorder.

Enhanced many-body localization in a kinetically constrained model.

In the study of the thermalization of closed quantum systems, the role of kinetic constraints on the temporal dynamics and the eventual thermalization is attracting significant interest. Kinetic constraints typically lead to long-lived metastable states depending on initial conditions. We consider a model of interacting hardcore bosons with an additional kinetic constraint that was originally devised to capture glassy dynamics at high densities. As a main result, we demonstrate that the system is highly prone to localization in the presence of uncorrelated disorder. Adding disorder quickly triggers long-lived dynamics as evidenced in the time evolution of density autocorrelations. Moreover, the kinetic constraint favors localization also in the eigenstates, where a finite-size transition to a many-body localized phase occurs for much lower disorder strengths than for the same model without a kinetic constraint. Our work sheds light on the intricate interplay of kinetic constraints and localization and may provide additional control over many-body localized phases in the time domain.

Exploring disorder correlations in superconducting systems: spectroscopic insights and matrix element effects.

Understanding the intricate interplay between disorder and superconductivity has become a key area of research in condensed matter physics, with profound implications for materials science. Recent studies have shown that spatial correlations of disorder potential can improve superconductivity, prompting a re-evaluation of some theoretical models. This paper explores the influence of disorder correlations on the fundamental properties of superconducting systems, going beyond the traditional assumption of spatially uncorrelated disorder. In particular, we investigate the influence of disorder correlations on key spectroscopic superconductor properties, including the density of states, as well as on the matrix elements of the superconducting coupling constant and their impact on the localization length. Our findings offer valuable insights into the role of disorder correlations in shaping the behavior of superconducting materials.

Strain-controlled charge and spin current rectifications in spin–orbit coupled graphene nano-ribbon: A new proposition

In this work, we investigate the possibilities of performing charge and spin current rectifications using graphene nano-ribbon in the presence of Rashba spin–orbit (SO) interaction. More specifically, we explore the specific role of mechanical strain on these two different types of current rectifications. The system is simulated by a tight-binding framework, where all the results are worked out based on the standard Green’s function formalism. In order to have current rectification, an asymmetry is required, which is incorporated through uncorrelated disorder among the constituent lattice points. From our extensive numerical analysis, we find that reasonably large charge and spin current rectifications can be obtained under strained conditions, and all the physical pictures are valid for a broad range of tight-binding parameters. The rectification properties are studied mostly for zigzag graphene nano-ribbons; however, an armchair ribbon is also taken into account for a clear comparison. Our work may provide a new direction of getting strain-controlled current rectifications in similar kinds of other physical systems as well.

Multiexciton spectra of molecular aggregates: application to photosynthetic antenna complexes.

We perform theoretical studies of nonlinear spectral responses of molecular aggregates upon multiple electronic excitations. It is shown that the transient absorption (TA) spectra exhibit gradual shifting to short wavelengths upon an increase in excitation energy accompanied by population of higher-order exciton manifolds. This transformation of the TA profile reflects a character of the exciton splitting and, therefore, is strongly dependent on the aggregate shape and size as well as on the exciton couplings and disorder of the site energies. The theory is applied for modeling of the intensity-dependent TA spectra of a light-harvesting LH1 antenna from a photosynthetic purple bacterium. Fitting of the data allowed verification of the exciton model of the complex (enabling us to differentiate between the correlated (elliptical) and uncorrelated energetic disorder). We found that the difference between the TA spectra corresponding to the absorption of one and two quanta suggests the presence of strong uncorrelated disorder (in agreement with earlier models of bacterial LH1/LH2 antennas). Nonlinear spectroscopy with multiple excitations may also be useful for exploring the exciton structure of other photosynthetic antennas and similar molecular systems.

Ion-Selective Scattering Studied Using the Variable-Energy Electron Irradiation in the Ba0.2K0.8Fe2As2 Superconductor.

Low-temperature variable-energy electron irradiation was used to induce non-magnetic disorder in a single crystal of a hole-doped iron-based superconductor, Ba1-xKxFe2As2, x = 0.80. To avoid systematic errors, the beam energy was adjusted non-consequently for five values between 1.0 and 2.5 MeV when sample resistance was measured in situ at 22 K. For all energies, the resistivity raises linearly with the irradiation fluence suggesting the creation of uncorrelated dilute point-like disorder (confirmed by simulations). The rate of the resistivity increase peaks at energies below 1.5 MeV. Comparison with calculated partial cross-sections points to the predominant creation of defects in the iron sublattice. Simultaneously, superconducting Tc, measured separately between the irradiation runs, is monotonically suppressed as expected, since it depends on the total scattering rate, hence on the total cross-section, which is a monotonically increasing function of the energy. Our work experimentally confirms an often-made assumption of the dominant role of the iron sub-lattice in iron-based superconductors.

Anderson localization without eigenstates in photonic quantum walks.

Anderson localization is ubiquitous in wavy systems with strong static and uncorrelated disorder. The delicate destructive interference underlying Anderson localization is usually washed out in the presence of temporal fluctuations or aperiodic drives in the Hamiltonian, leading to delocalization and restoring transport. However, in one-dimensional lattices with off diagonal disorder, Anderson localization can persist for arbitrary time-dependent drivings that do not break a hidden conservation law originating from the chiral symmetry, leading to the dubbed "localization without eigenstates." Here it is shown that such an intriguing phenomenon can be observed in discrete-time photonic quantum walks with static disorder applied to the coin operator and can be extended to non-Hermitian dynamics as well.

Anderson Localization in Dissipative Lattices

AbstractAnderson localization predicts that wave spreading in disordered lattices can come to a complete halt, providing a universal mechanism for dynamical localization. In the one‐dimensional Hermitian Anderson model with uncorrelated diagonal disorder, there is a one‐to‐one correspondence between dynamical localization and spectral localization, that is, the exponential localization of all the Hamiltonian eigenfunctions. This correspondence can be broken when dealing with disordered dissipative lattices. When the system exchanges particles with the surrounding environment and random fluctuations of the dissipation are introduced, spectral localization is observed but without dynamical localization. Previous studies consider lattices with mixed conservative (Hamiltonian) and dissipative dynamics and are restricted to a semiclassical analysis. However, Anderson localization in purely dissipative lattices, displaying an entirely Lindbladian dynamics, remains largely unexplored. Here the purely‐dissipative Anderson model in the framework of a Lindblad master equation is considered, and it is shown that, akin to the semiclassical models with conservative hopping and random dissipation, one observes dynamical delocalization in spite of strong spectral localization of the Liouvillian superoperator. This result is very distinct from delocalization observed in the Anderson model with dephasing, where dynamical delocalization arises from the delocalization of the stationary state of the Liouvillian.

Unidirectional scattering with spatial homogeneity using correlated photonic time disorder

Recently, there has been increasing interest in the temporal degree of freedom in photonics due to its analogy with spatial axes, causality and open-system characteristics. In particular, the temporal analogues of photonic crystals have allowed the design of momentum gaps and their extension to topological and non-Hermitian photonics. Although recent studies have also revealed the effect of broken discrete time-translational symmetry in view of the temporal analogy of spatial Anderson localization, the broad intermediate regime between time order and time uncorrelated disorder has not been examined. Here we theoretically investigate the inverse design of photonic time disorder to achieve optical functionalities in spatially homogeneous platforms. By developing the structure factor and order metric using causal Green’s functions for disorder in the time domain, we propose an engineered time scatterer, which provides unidirectional scattering with controlled scattering amplitudes. We also show that the order-to-disorder transition in the time domain allows the manipulation of scattering bandwidths, which makes resonance-free temporal colour filtering possible. Our work could advance optical functionalities without spatial patterning.

Rogue waves in quantum lattices with correlated disorder

We investigate the outbreak of anomalous quantum wave-function amplitudes in a one-dimensional tight-binding lattice featuring correlated diagonal disorder. Such rogue-wave-like behavior is fostered by a competition between localization and mobility. The effective correlation length of the disorder is ultimately responsible for bringing the local disorder strength to a minimum, fueling the occurrence of extreme events of much higher amplitudes, especially when compared to the case of uncorrelated disorder. Our findings are valid for a class of discrete one-dimensional systems and reveal profound aspects of the role of randomness in rogue-wave generation.

Unconventional delocalization in a family of three-dimensional Lieb lattices

Uncorrelated disorder in generalized 3D Lieb models gives rise to the existence of bounded mobility edges, destroys the macroscopic degeneracy of the flat bands and breaks their compactly-localized states. We now introduce a mix of order and disorder such that this degeneracy remains and the compactly-localized states are preserved. We obtain the energy-disorder phase diagrams and identify mobility edges. Intriguingly, for large disorder the survival of the compactly-localized states induces the existence of delocalized eigenstates close to the original flat band energies -- yielding seemingly divergent mobility edges. For small disorder, however, a change from extended to localized behavior can be found upon decreasing disorder -- leading to an unconventional ``inverse Anderson" behavior. We show that transfer matrix methods, computing the localization lengths, as well as sparse-matrix diagonalization, using spectral gap-ratio energy-level statistics, are in excellent quantitative agreement. The preservation of the compactly-localized states even in the presence of this disorder might be useful for envisaged storage applications.

Weak quantization of noninteracting topological Anderson insulator

We study the transition between the two-dimensional topological insulator (TI) featuring quantized edge conductance and the trivial Anderson insulator (AI) induced by strong disorder. We discover a distinct scaling behavior of TI near the phase transition where the longitudinal conductance approaches the quantized value by a power law with system size, instead of an exponential law in clean TI. This region is thus called the weak quantization topological insulator (WQTI). By using the self-consistent Born approximation, we associate the emergence of the weak quantization with the imaginary part of the effective self-energy acquiring a finite value at strong disorder. We use our analytical theory, supported by direct numerical simulations, to study the effect of disorder range on the topological Anderson insulator. Interestingly, while this phase is quite generic for uncorrelated or short-range disorder, it is strongly suppressed by long-range disorder, perhaps explaining why it has never been seen in solid state systems.

Disorder-induced topological phase transition in HgCdTe crystals

Using the self-consistent Born approximation, we study a topological phase transition appearing in bulk HgCdTe crystals induced \emph{uncorrelated} disorder due to both randomly distributed impurities and fluctuations in Cd composition. By following the density-of-states evolution, we clearly demonstrate the topological phase transition, which can be understood in terms of the disorder-renormalized mass of Kane fermions. We find that the presence of heavy-hole band in HgCdTe crystals leads to the topological phase transition at much lower disorder strength than it is expected for conventional 3D topological insulators. Our theoretical results can be also applied to other narrow-gap zinc-blende semiconductors such as InAs, InSb and their ternary alloys InAsSb.

Wave transport in stealth hyperuniform materials: The diffusive regime and beyond

By varying the degree of correlation in stealthy hyperuniform (SHU) materials, the continuous evolution from uncorrelated disorder to periodic media is possible and allows us, as such, to study the fate of the bimodal distribution, the characteristic of a diffusive transport. Considering the wave transport through a SHU distribution of a given number of scatterers and at a given frequency, the transition from a diffusive to a transparent medium is clearly observed only below the Bragg frequency. This transition is characterized by a threshold value of the stealthiness at the vicinity of which the material abruptly changes from diffusive to transparent. In contrast, no such clear transition is observed at or above the Bragg frequency and, surprisingly, a seemingly bimodal distribution of the transmission eigenvalues still characterizes the SHU materials, even when strongly correlated.