Disorder Strength Research Articles

Mapping the topology-localization phase diagram with quasiperiodic disorder using a programmable superconducting simulator

We explore a topology-localization phase diagram by simulating a one-dimensional Su-Schrieffer-Heeger model with quasiperiodic disorder using a programmable superconducting simulator. We experimentally map out and identify various trivial and topological phases with extended, critical, and localized bulk states. We find that with increasing disorder strength, some extended states can be first replaced by localized states and then by critical states before the system finally becomes fully localized. The critical states exhibit typical features such as multifractality and self-similarity, which lead to surprisingly rich phases with different types of mobility edges and scaling behaviors on the phase boundaries. Our results shed light on the investigation of the topological and localization phenomena in condensed-matter physics. Published by the American Physical Society 2024

Modulating the Electrical Transport in Superconducting NbC Crystals by Fractal Morphology.

The self-similar fractal morphology mediated by nonequilibrium processes is widely observed in low-dimensional materials grown by various techniques. Understanding how these fractal geometries affect the physical and chemical properties of materials and devices is crucial for both fundamental studies and various applications. In particular, the interplay between superconducting phase fluctuations and disorder can give rise to intriguing phenomena depending on the dimensionality. However, current experimental studies on low-dimensional superconductors are limited to two- and one-dimensional systems, leaving fractional dimensional systems largely unexplored. Here, we use chemical vapor deposition to successfully synthesize ultrathin NbC crystals with a well-defined fractal geometry at the nanoscale. By performing electrical transport measurements, we find that both the superconducting and normal-state properties are strongly affected in the fractal samples, where the intrinsic and geometric disorder is induced. In contrast to the 2D crystal, the fractal NbC crystals show a significant low-temperature resistive upturn before the onset of superconducting transition, which can be attributed to the disorder-enhanced electron-electron interaction effect. From transport data analysis, we demonstrate that the superconducting transition in NbC is correlated to the strength of disorder and the fractional dimensions, revealing that nanoscale fractal structures can significantly modify the electronic properties of low-dimensional superconductors. Our work paves the way for the explorations of mesoscopic transport and intriguing superconducting phenomena in fractional dimensions.

Percolation versus depinning transition: The inherent role of damage hardening during quasibrittle failure.

The intermittent damage evolution preceding the failure of heterogeneous brittle solids is well described by scaling laws. In deciphering its origins, failure is routinely interpreted as a critical transition. However at odds with expectations of universality, a large scatter in the value of the scaling exponents is reported during acoustic emission experiments. Here we numerically examine the precursory damage activity to reconcile the experimental observations with critical phenomena framework. Along with the strength of disorder, we consider an additional parameter that describes the progressive damageability of material elements at mesoscopic scale. This hardening behavior encapsulates the microfracturing processes taking place at lower length scales. We find that damage hardening can not only delay the final failure but also affect the preceding damage accumulation. When hardening is low, the precursory activity is strongly influenced by the strength of the disorder and is reminiscent of damage percolation. On the contrary, for large hardening, long-range elastic interactions prevail over disorder, ensuring a rather homogeneous evolution of the damage field in the material. The power-law statistics of the damage bursts is robust to the strength of the disorder and is reminiscent of the collective avalanche dynamics of elastic interfaces near the depinning transition. The existence of these two distinct universality classes also manifests as different values of the scaling exponent characterizing the divergence of the precursor size on approaching failure. Our finding sheds new light on the connection between the level of quasibrittleness of materials and the statistical features of the failure precursors. Finally, it also provides a more complete description of the acoustic precursors and thus paves the way for quantitative techniques of damage monitoring of structures-in-service.

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.

Unified theory for the scaling of the crossover between strong and weak disorder behaviors of optimal paths and directed or undirected polymers in disordered media.

In this paper, we are concerned with the crossover between strong disorder (SD) and weak disorder (WD) behaviors in three well-known problems that involve minimal paths: directed polymers (directed paths with fixed starting point and length), optimal paths (undirected paths with a fixed end-to-end or spanning distance), and undirected polymers (undirected paths with a fixed starting point and length). We present a unified theoretical framework from which we can easily deduce the scaling of the crossover point of each problem in an arbitrary dimension. Our theory is based on the fact that the SD limit behavior of these systems is closely related to the corresponding percolation problem. As a result, the properties of those minimal paths are completely controlled by the so-called red bonds of percolation theory. Our model is first addressed numerically and then approximated by a two-term approach. This approach provides us with an analytical expression that seems to be reasonably accurate. The results are in perfect agreement with our simulations and with most of the results reported in related works. Our research also leads us to propose this crossover point as a universal measure of the disorder strength in each case. Interestingly, that measure depends on both the statistical properties of the disorder and the topological properties of the network.

Power-law localization in one-dimensional systems with nonlinear disorder under fixed input conditions

We conduct a numerical investigation into wave propagation and localization in one-dimensional lattices subject to nonlinear disorder, focusing on cases with fixed input conditions. Utilizing a discrete nonlinear Schrödinger equation with Kerr-type nonlinearity and a random coefficient, we compute the averages and variances of the transmittance, T, and its logarithm, as functions of the system size L, while maintaining constant intensity for the incident wave. In cases of purely nonlinear disorder, we observe power-law localization characterized by 〈T〉∝L−γa and 〈lnT〉≈−γglnL for sufficiently large L. At low input intensities, a transition from exponential to power-law decay in 〈T〉 occurs as L increases. The exponents γa and γg are nearly identical, converging to approximately 0.5 as the strength of the nonlinear disorder, β, increases. Additionally, the variance of T decays according to a power law with an exponent close to 1, and the variance of lnT approaches a small constant as L increases. These findings are consistent with an underlying log-normal distribution of T and suggest that wave propagation behavior becomes nearly deterministic as the system size increases. When both linear and nonlinear disorders are present, we observe a transition from power-law to exponential decay in transmittance with increasing L when the strength of linear disorder, V, is less than β. As V increases, the region exhibiting power-law localization diminishes and eventually disappears when V exceeds β, leading to standard Anderson localization.

Critical crack length during fracture.

Through controlled numerical simulations in a one-dimensional fiber bundle model with local stress concentration, we established an inverse correlation between the strength of the material and the cracks which grow inside it-both the maximum crack and the one that sets in instability within the system, defined to be the critical crack. Through the Pearson correlation function as well as probabilistic study of individual configurations, we found that the maximum and the critical crack often differ from each other unless the disorder strength is extremely low. A phase diagram on the plane of disorder vs system size demarcates between the regions where the largest crack is the most vulnerable one and where they differ from each other but still show moderate correlation.

Disordered non-Fermi liquid fixed point for two-dimensional metals at Ising-nematic quantum critical points

Understanding the influence of quenched random potential is crucial for comprehending the exotic electronic transport of non-Fermi liquid metals near metallic quantum critical points. In this study, we identify a stable fixed point governing the quantum critical behavior of two-dimensional non-Fermi liquid metals in the presence of a random potential disorder. By performing renormalization group analysis on a dimensional-regularized field theory for Ising-nematic quantum critical points, we systematically investigate the interplay between random potential disorder for electrons and Yukawa-type interactions between electrons and bosonic order-parameter fluctuations in a perturbative epsilon expansion. At the one-loop order, the effective field theory lacks stable fixed points, instead exhibiting a runaway flow toward infinite disorder strength. However, at the two-loop order, the effective field theory converges to a stable fixed point characterized by finite disorder strength, termed the “disordered non-Fermi liquid (DNFL) fixed point”. Our investigation reveals that two-loop vertex corrections induced by Yukawa couplings are pivotal in the emergence of the DNFL fixed point, primarily through screening disorder scattering. Additionally, the DNFL fixed point is distinguished by a substantial anomalous scaling dimension of fermion fields, resulting in pseudogap-like behavior in the electron’s density of states. These findings shed light on the quantum critical behavior of disordered non-Fermi liquid metals, emphasizing the indispensable role of higher-order loop corrections in such comprehension.

TD-DMRG Study of Exciton Dynamics with both Thermal and Static Disorders for Fenna-Matthews-Olson Complex.

Photosynthesis is a fundamental process that converts solar energy into chemical energy. Understanding the microscopic mechanisms of energy transfer in photosynthetic systems is crucial for the development of novel optoelectronic materials. Simulating these processes poses significant challenges due to the intricate interactions between electrons and phonons, compounded by static disorder. In this work, we present a numerically nearly exact study using the time-dependent density matrix renormalization group (TD-DMRG) method to simulate the quantum dynamics of the Fenna-Matthews-Olson (FMO) complex considering an eight-site model with both thermal and static disorders. We employ the thermo-field dynamics formalism for temperature effects. We merge all electronic interactions into one large matrix product state (MPS) site, boosting accuracy efficiently without increasing complexity. Previous combined experimental and computational studies indicated that the static disorders range from 30 to 90 cm-1 for different FMO sites. We employ a Gaussian distribution and the auxiliary bosonic operator approach to consider the static disorder in our TD-DMRG algorithm. We investigate the impact of different initial excitation sites, temperatures, and degrees of static disorder on the exciton dynamics and temporal coherence. It is found that under the influence of the experimentally determined static disorder strength, the exciton population evolution shows a non-negligible difference at zero temperature, while it is hardly affected at room temperature.

Topological tight binding models on some non-trivial lattices: union of geometry, flat bands and topology

We introduce a topological tight binding model based on certain rules that we have formulated to study systems with certain non-trivial bulks. These rules allow us to study bulks that have twists and branching. We discuss certain cases in the SAB model with different number of bands, exhibiting several interesting physical properties. For every bulk there can be two sets of configurations: the orientable and the non-orientable configuration. The later exhibits several non-trivial physical properties like exact flat bands (exactly at particle hole symmetry level), zero energy states localised in the bulk, topological edge states etc. We then discuss a three band non-orientable SAB model which is easy to visualise. We also investigate the effects of disorder (both chiral symmetry preserving and breaking) in the non-orientable configurations hosting flat bands. We find for chiral symmetry preserving disorders, some of them (non-degenerate flat band) are robust to large disorders while others (degenerate flat band) exhibit an insulator to metal transition beyond certain critical disorder strength due to band gap closing as a result of the broadening of the zero energy states. For chiral symmetry breaking disorders, in both the cases the zero energy bulk states broaden and close the gap beyond certain critical disorder strength.

Anderson Localization Transition in Disordered Hyperbolic Lattices.

We study Anderson localization in disordered tight-binding models on hyperbolic lattices. Such lattices are geometries intermediate between ordinary two-dimensional crystalline lattices, which localize at infinitesimal disorder, and Bethe lattices, which localize at strong disorder. Using state-of-the-art computational group theory methods to create large systems, we approximate the thermodynamic limit through appropriate periodic boundary conditions and numerically demonstrate the existence of an Anderson localization transition on the {8,3} and {8,8} lattices. We find unusually large critical disorder strengths, determine critical exponents, and observe a strong finite-size effect in the level statistics.

Statistics of Lyapunov exponent in random Fibonacci multilayer

Abstract We numerically investigated the localization properties of band-gap and band-edge modes in a one-dimensional random Fibonacci optical multilayer. The statistics of the Lyapunov Exponent (LE) reveal distinct behaviors of localization effects for band-edge and band-gap modes as a function of disorder strength. In particular, a deviation from the single parameter scaling theory (SPST) of localization was observed within a frequency window corresponding to the band-gap of an ordered Fibonacci multilayer. To provide a physical explanation for the violation of SPST, a close correlation between the frequency distribution of the resonant modes in the band-gap and the variance of the LE has been found. The spatial distribution of resonant modes has been reported and discussed. Finally, the dynamics of the gap closing of the two main band-gaps as a function of the disorder strength has been analyzed.

Density matrix renormalization group study of the interacting Kitaev chain with quasi-periodic disorder

We document the ground state phase diagram of the one-dimensional Kitaev chain with quasi-periodic disorder in the presence of two-body interactions. Our data were obtained for systems of L=1000\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L=1000$$\\end{document} sites using large-scale density-matrix renormalization group numerics and is benchmarked against known results for the clean system. We demonstrate that moderate quasi-periodic disorder stabilizes the topological phase both for repulsive and attractive interactions. For larger disorder strengths, the system features re-entrance behavior and multiple phase transitions.Graphical abstractPhase diagram as a function of the chemical potential and the disorder strength for repulsive interactions

Large-deviations approach to thermalization: the case of harmonic chains with conservative noise

We investigate the possibility of characterizing the different thermalization pathways through a large-deviation approach. Specifically, we consider clean, disordered and quasi-periodic harmonic chains under energy and momentum-conserving noise. For their associated master equations, describing the dynamics of normal modes energies, we compute the fluctuations of activity and dynamical entropy in the corresponding biased ensembles. First-order dynamical phase transition are found that originates from different activity regions in action space. At the transitions, the steady-state in the biased ensembles changes from extended to localized, yielding a kind of condensation in normal-modes space. For the disordered and quasi-periodic models, we argue that the phase-diagram has a critical point at a finite value of the disorder or potential strength.

Thermoelectric Phenomena in a Magnetic Heterostructure with AAH Modulation: Charge and Spin Figure of Merits

ABSTRACT We put forward a prescription of getting a higher value of the spin-dependent figure of merit in comparison with its charge counterpart in the case of a 1D magnetic heterostructure (a ferromagnetic (FM) chain sandwiched between two non-magnetic 1D lattices) where all the site energies of the heterostructure follow cosine form of modulation defined in Aubry-Andre-Harper (AAH) model. It is shown that due to having a greater number of non-uniform peaks in its transmission spectra, the thermoelectric efficiency of this heterostructure becomes superior compared to that is obtained in a fully ferromagnetic 1D chain. It is also reported that the maximum value of the thermoelectric figure of merit (for both spin and charge-dependent cases) of the heterostructure in a specified energy range gets enhanced in a continuous manner as the disorder strength of the AAH modulation is increased. The Hamiltonian of the proposed quantum system is described within a tight-binding (TB) framework and after the evaluation of transmission probability by utilizing the non-equilibrium Green’s function (NEGF) technique, all the important thermoelectric quantities are determined on the basis of Landauer formalism. We believe that our study on this particular topic of spin caloritronics, a subject associated with temperature-dependent spin transmission through a quantum channel, may help to explore several fascinating ideas about spin-related thermoelectric efficiency in many other ferromagnetic quasicrystals.

Characterizing localization effects in an ultracold disordered Fermi gas by diffusion analysis

Disorder can fundamentally modify the transport properties of a system. A striking example is Anderson localization, suppressing transport due to destructive interference of propagation paths. In inhomogeneous many-body systems, not all particles are localized for finite-strength disorder, and the system can become partially diffusive. Unraveling the intricate signatures of localization from such observed diffusion is a longstanding problem. Here, we experimentally study a degenerate, spin-polarized Fermi gas in a disorder potential formed by an optical speckle pattern. We record the diffusion through the disordered potential upon release from an external confining potential. We compare different methods to analyze the resulting density distributions, including a new approach to capture particle dynamics by evaluating absorption-image statistics. Using standard observables, such as diffusion exponent and coefficient, localized fraction, or localization length, we find that some show signatures for a transition to localization above a critical disorder strength, while others show a smooth crossover to a modified diffusion regime. In laterally displaced disorder, we spatially resolve different transport regimes simultaneously, which allows us to extract the subdiffusion exponent expected for weak localization. Our work emphasizes that the transition toward localization can be investigated by closely analyzing the system's diffusion, offering ways of revealing localization effects beyond the signature of exponentially decaying density distribution. Published by the American Physical Society 2024

Emergence of quantum Griffiths singularity in disordered TiN thin films

The association of quantum Griffiths singularity (QGS) to the magnetic-field-induced superconductor-metal transition predicts the unconventional diverging behaviour of dynamical critical exponent in low disorder crystalline two-dimensional superconductors. But whether this state exists in the superconducting systems exhibiting superconductor-insulator transition remains elusive. Here, we report the emergence of quantum Griffiths singularity in ultrathin disordered TiN thin films with more than two orders of magnitude variation in their normal state resistance. For both superconductor-metal transition and superconductor-insulator transition types, a diverging critical exponent is observed while approaching the quantum phase transition. Further, the magnetoresistance isotherms obey a direct activated scaling governed by an infinite-randomness fixed critical point. Finally, this work establishes the robustness of the QGS phenomenon towards a wide range of temperature and also towards a wide range of disorder strength as correlated with the normal state resistance.

Assessment of Changes in Behavior and Quality of Life after Monobloc Treatment in Children with Obstructive Sleep Apnea or Primary Snoring.

The aim of this study was to examine the quality of life and behavioral disorders in children with obstructive sleep apnea (OSA) or primary snoring, as well as how these problems changed after monobloc treatment. Fourteen children with primary snoring and 16 children with OSA who had skeletal class II malocclusion due to mandibular retrognathia were treated with monobloc appliances. To investigate the relationship between behavioral disorders and quality of life, parents were asked to complete four questionnaires: attention deficit and hyperactivity disorder (ADHD) scale, strength and difficulties questionnaire (SDQ), pediatric sleep questionnaire (PSQ), and Pittsburgh sleep quality scale (PSQS). Mann-Whitney U and Wilcoxon signed-rank tests were used to evaluate the data. According to the results of the PSQ and PSQS, an increase in sleep quality was observed after monobloc treatment. The decrease in the total ADHD score at the end of the treatment was found to be statistically significant in both the OSA (p<0.01) and snoring (p<0.01) groups. According to the SDQ scores, the increase in the social behavior score and the decrease in the peer bullying score in the snoring group were statistically significant (p<0.05). The use of a monobloc appliance in pediatric patients exhibiting primary snoring and OSA resulted in a notable reduction in sleep-breathing disorder symptoms and a notable enhancement in their overall quality of life. Based on the analyses of the questionnaires, it was concluded that the increase in sleep quality improved the pediatric patients' quality of life after orthodontic treatment with orthodontic monobloc appliances.

Anderson localized transport in non-Hermitian spoof surface plasmon polariton structures

Anderson localization, a fundamental wave phenomenon, is a challenging problem in quasiparticle transport, exacerbated in the presence of dissipation. Of late, however, a few demonstrations of Anderson localization in non-Hermitian structures have been made. In the domain of electromagnetics of structured materials, spoof surface plasmon polaritons are a very interesting concept where structured metallic surfaces sustain bound states even at very low frequencies. The metallic non-Hermiticity, in an environment of possible disorder, makes this system an interesting case-study for mesoscopic transport, although the idea of disordered structures for spoof plasmons is not commonly encountered in literature. Here, we present experimental evidence of Anderson localization in hybrid polariton–photon states within a disordered, non-Hermitian environment. Disorder is introduced by perturbing the periodic microstructure while maintaining surface confinement. Localization enhances the plasmonic intensity by about a factor of three as compared to the conventional periodic structure. We experimentally characterize the intensity distribution, dispersion properties, and generalized conductance within the Anderson localized regime. A significant decrease in both localization length and its fluctuations is observed with increasing disorder strength. The inverse participation ratio shows the anticipated linear dependency on localization length. Our results offer experimental proof of Anderson localization in hybrid polariton–photon states, showcasing the influence of disorder in boosting plasmonic intensity. This elucidates potential applications in fields requiring controlled wave transport in disordered settings.

Effects of forward disorder on quasi-one-dimensional superconductors

We study the competition between disorder and singlet superconductivity in a quasi-one-dimensional (1D) system. We investigate the applicability of the Anderson theorem, namely that time-reversal conserving (nonmagnetic) disorder does not impact the critical temperature, by opposition to time-reversal breaking disorder (magnetic). To do so, we examine a quasi-1D system of spin 1/2 fermions with attractive interactions and forward scattering disorder using field theory (bosonization). By computing the superconducting critical temperature (Tc), we find that, for nonmagnetic disorder, the Anderson theorem also holds in the quasi-1D geometry. In contrast, magnetic disorder has an impact on the critical temperature, which we investigate by deriving renormalization group equations describing the competition between disorder and interactions. Computing the critical temperature as a function of disorder strength, we observe different regimes depending on the strength of interactions. We discuss possible platforms where this can be observed in cold atoms and condensed matter. Published by the American Physical Society 2024