Translational Order Research Articles

Extreme Electron-Photon Interaction in Disordered Perovskites.

The interaction of light with solids can be dramatically enhanced owing to electron-photon momentum matching. This mechanism manifests when light scattering from nanometer-sized clusters including a specific case of self-assembled nanostructures that form a long-range translational order but local disorder (crystal-liquid duality). In this paper, a new strategy based on both cases for the light-matter-interaction enhancement in a direct bandgap semiconductor - lead halide perovskite CsPbBr3 - by using electric pulse-driven structural disorder, is addressed. The disordered state allows the generation of confined photons, and the formation of an electronic continuum of static/dynamic defect states across the forbidden gap (Urbach bridge). Both mechanisms underlie photon-momentum-enabled electronic Raman scattering (ERS) and single-photon anti-Stokes photoluminescence (PL) under sub-band pump. PL/ERS blinking is discussed to be associated with thermal fluctuations of cross-linked [PbBr6]4- octahedra. Time-delayed synchronization of PL/ERS blinking causes enhanced spontaneous emission at room temperature. These findings indicate the role of photon momentum in enhanced light-matter interactions in disordered and nanostructured solids.

Chirality and odd mechanics in active columnar phases.

Chiral active materials display odd dynamical effects in both their elastic and viscous responses. We show that the most symmetric mesophase with 2D odd elasticity in three dimensions is chiral, polar, and columnar, with 2D translational order in the plane perpendicular to the columns and no elastic restoring force for their relative sliding. We derive its hydrodynamic equations from those of a chiral active variant of model H. The most striking prediction of the odd dynamics is two distinct types of column oscillation whose frequencies do not vanish at zero wavenumber. In addition, activity leads to a buckling instability coming from the generic force-dipole active stress analogous to the mechanical Helfrich-Hurault instability in passive materials, while the chiral torque-dipole active stress fundamentally modifies the instability by the selection of helical column undulations.

Liquid-Crystal-Like Dynamic Transition in Ferroelectric-Dielectric Superlattices.

Nanostructured ferroelectrics display exotic multidomain configurations resulting from the electrostatic and elastic boundary conditions they are subject to. While the ferroelectric domains appear frozen in experimental images, atomistic second-principles studies suggest that they may become spontaneously mobile upon heating, with the polar order melting in a liquidlike fashion. Here, we run molecular dynamics simulations of model systems (PbTiO_{3}/SrTiO_{3} superlattices) to study the unique features of this transformation. Most notably, we find that the multidomain state loses its translational and orientational orders at different temperatures, resembling the behavior of liquid crystals and yielding an intermediate hexaticlike phase. Our simulations reveal the mechanism responsible for the melting and allow us to characterize the stochastic dynamics in the hexaticlike phase: we find evidence that it is thermally activated, with domain reorientation rates that grow from tens of gigahertzs to terahertzs in a narrow temperature window.

Enhancing (quasi-)long-range order in a two-dimensional driven crystal.

It has been recently shown that 2D systems can exhibit crystalline phases with long-range translational order showcasing a striking violation of the Hohenberg-Mermin-Wagner (HMW) theorem, which is valid at equilibrium. This is made possible by athermal driving mechanisms that inject energy into the system without exciting long wavelength modes of the density field, thereby inducing hyperuniformity. However, as thermal fluctuations are superimposed on the non-equilibrium driving, long-range translational order is inevitably lost. Here, we discuss the possibility of exploiting non-equilibrium effects to suppress arbitrarily large density fluctuations even when a global thermal bath is coupled to the system. We introduce a model of a harmonic crystal driven both by a global thermal bath and by a momentum conserving noise, where the typical observables related to density fluctuations and long-range translational order can be analytically derived and put in relation. This model allows us to rationalize the violation of the HMW theorem observed in previous studies through the prediction of large-wavelength phonons, which thermalize at a vanishing effective temperature when the global bath is switched off. The conceptual framework introduced through this theory is then applied to numerical simulations of a hard-disk solid in contact with a thermal bath and driven out-of-equilibrium by active collisions. Our numerical analysis demonstrates how varying driving and dissipative parameters can lead to an arbitrary enhancement of the quasi-long-range order in the system regardless of the applied global noise amplitude. Finally, we outline a possible experimental procedure to apply our results to a realistic granular system.

How near-field photon momentum drives unusual optical phenomena: opinion

This Opinion article discusses the fundamental role of the near-field photon momentum in processes of light scattering from nanometer-sized clusters including an intriguing case of self-assembled nanostructures that form a long-range translational order but local disorder. Systems exhibiting the so-called crystal-liquid duality enable greatly enhanced light-matter interactions due to the electron-photon momentum matching in the visible wavelength range. This work takes a historical perspective on the exploration of this phenomenon that has been somewhat overlooked by the scientific community and discusses recent advances in the fields of nonlocal photonics and optoelectronics.

Hyperuniformity classes of quasiperiodic tilings via diffusion spreadability.

Hyperuniform point patterns can be classified by the hyperuniformity scaling exponent α>0, that characterizes the power-law scaling behavior of the structure factor S(k) as a function of wave number k≡|k| in the vicinity of the origin, e.g., S(k)∼|k|^{α} in cases where S(k) varies continuously with k as k→0. In this paper, we show that the spreadability is an effective method for determining α for quasiperiodic systems where S(k) is discontinuous and consists of a dense set of Bragg peaks. It has been shown in [Phys. Rev. E 104, 054102 (2021)10.1103/PhysRevE.104.054102] that, for media with finite α, the long-time behavior of the excess spreadability S(∞)-S(t) can be fit to a power law of the form t^{-(d-α)/2}, where d is the space dimension, to accurately extract α for the continuous case. We first transform quasiperiodic and limit-periodic point patterns into two-phase media by mapping them onto packings of identical nonoverlapping disks, where space interior to the disks represents one phase and the space in exterior to them represents the second phase. We then compute the spectral density χ[over ̃]_{_{V}}(k) of the packings, and finally compute and fit the long-time behavior of their excess spreadabilities. Specifically, we show that the excess spreadability can be used to accurately extract α for the one-dimensional (1D) limit-periodic period-doubling chain (α=1) and the 1D quasicrystalline Fibonacci chain (α=3) to within 0.02% of the analytically known exact results. Moreover, we obtain a value of α=5.97±0.06 for the two-dimensional Penrose tiling and present plausible theoretical arguments strongly suggesting that α is exactly equal to six. We also show that, due to the self-similarity of the structures examined here, one can truncate the small-k region of the scattering information used to compute the spreadability and obtain an accurate value of α, with a small deviation from the untruncated case that decreases as the system size increases. This strongly suggests that one can obtain a good estimate of α for an infinite self-similar quasicrystal from a modestly sized finite sample. The methods described here offer a simple and general procedure to characterize accurately the large-scale translational order present in quasicrystalline and limit-periodic media in any space dimension that are self-similar. Moreover, the scattering information extracted from these two-phase media encoded in χ[over ̃]_{_{V}}(k), can be used to estimate their physical properties, such as their effective dynamic dielectric constants, effective dynamic elastic constants, and fluid permeabilities.

A simple model for density anomaly and excess thermodynamic properties of alcohol-like in water-like mixture

ABSTRACT Molecular dynamics simulations were employed to gain insights into the density anomaly and excess thermodynamic properties of a binary mixture composed of a solvent resembling water and a solute resembling alcohol. In our model, both fluids were represented by spherical particles interacting through effective potentials: a two-length scale potential for the solvent–solvent interaction while purely repulsive potentials were used for the solute–solute and solute–solvent interactions. The temperature of maximum density (TMD) present in the pure solvent system is also observed in our mixture. The TMD exhibits a positive deviation in the mixture when compared to the pure solvent fluid under high-pressure conditions, while it shows a negative deviation under low-pressure conditions what is consistent with experiments. The excess volume, enthalpy and isobaric heat capacity show extreme values at x ≈ 0.4 . Using the radial distribution function and the translational order parameter we suggest that this behaviour can be explained in terms of solute particles caged in solvent network.

Cell Division and Motility Enable Hexatic Order in Biological Tissues.

Biological tissues transform between solid- and liquidlike states in many fundamental physiological events. Recent experimental observations further suggest that in two-dimensional epithelial tissues these solid-liquid transformations can happen via intermediate states akin to the intermediate hexatic phases observed in equilibrium two-dimensional melting. The hexatic phase is characterized by quasi-long-range (power-law) orientational order but no translational order, thus endowing some structure to an otherwise structureless fluid. While it has been shown that hexatic order in tissue models can be induced by motility and thermal fluctuations, the role of cell division and apoptosis (birth and death) has remained poorly understood, despite its fundamental biological role. Here we study the effect of cell division and apoptosis on global hexatic order within the framework of the self-propelled Voronoi model of tissue. Although cell division naively destroys order and active motility facilitates deformations, we show that their combined action drives a liquid-hexatic-liquid transformation as the motility increases. The hexatic phase is accessed by the delicate balance of dislocation defect generation from cell division and the active binding of disclination-antidisclination pairs from motility. We formulate a mean-field model to elucidate this competition between cell division and motility and the consequent development of hexatic order.

Dynamic Transformation of High-Architectural Nanocrystal Superlattices upon Solvent Molecule Exposure.

The cluster-based body-centered-cubic superlattice (cBCC SL) represents one of the most complicated structures among reported nanocrystal assemblies, comprised of 72 truncated tetrahedral quantum dots per unit cell. Our previous report revealed that truncated tetrahedral quantum dots within cBCC SLs possessed highly controlled translational and orientational order owing to an unusual energetic landscape based on the balancing of entropic and enthalpic contributions during the assembly process. However, the cBCC SL's structural transformability and mechanical properties, uniquely originating from such complicated nanostructures, have yet to be investigated. Herein, we report that cBCC SLs can undergo dynamic transformation to face-centered-cubic SLs in response to post-assembly molecular exposure. We monitored the dynamic transformation process using in situ synchrotron-based small-angle X-ray scattering, revealing a dynamic transformation involving multiple steps underpinned by interactions between incoming molecules and TTQDs' surface ligands. Furthermore, our mechanistic study demonstrated that the precise configuration of TTQDs' ligand molecules in cBCC SLs was key to their high structural transformability and unique jelly-like soft mechanical properties. While ligand molecular configurations in nanocrystal SLs are often considered minor features, our findings emphasize their significance in controlling weak van der Waals interactions between nanocrystals within assembled SLs, leading to previously unremarked superstructural transformability and unique mechanical properties. Our findings promote a facile route toward further creation of soft materials, nanorobotics, and out-of-equilibrium assemblies based on nanocrystal building blocks.

Optimization of the Domain Size in Stressed Liquid Crystals

The distributions of orientational and translational order parameters in liquid crystal polymer composites are studied using the methods of molecular-statistical physics. A model is considered in which the composite consists of liquid crystal (LC) domains separated by flat polymer sheets. The perturbation of the orientational and translational order parameters, which is caused by an arbitrary flat polymer sheet in a planar LC layer, is estimated. The effective distance over which this disturbance propagates is estimated. It is shown that it is proportional to the square root of the splay elastic constant of LC. It has been shown that in certain temperature ranges the polymer can induce a more ordered liquid crystal phase near itself (smectic phase inside of nematic phase and nematic phase – inside of isotropic liquid phase). In this case, the orientational order parameter of LC near the polymer can be significantly higher than far from it, and the “perturbation” of the order parameters can propagate over a distance of up to several micrometers with a sharp peak at a distance of the order of one micrometer. Based on the original theory, the methods have been proposed for optimizing the sizes of domains in stressed liquid crystals obtained by mechanical treatment in liquid crystal polymer composites.

Fluid fibers in true 3D ferroelectric liquids

We demonstrate an exceptional ability of a high-polarization 3D ferroelectric liquid to form freely suspended fluid fibers at room temperature. Unlike fluid threads in modulated smectics and columnar phases, where translational order is a prerequisite for forming liquid fibers, recently discovered ferroelectric nematic forms fibers with solely orientational molecular order. Additional stabilization mechanisms based on the polar nature of the mesophase are required for this. We propose a model for such a mechanism and show that these fibers demonstrate an exceptional nonlinear optical response and exhibit electric field-driven instabilities.

Multiscale defect cluster excitations in the melting transitions of two-dimensional Yukawa systems

In this work, we numerically demonstrate and classify the intermittently emerged multiscale defect clusters (DCs) composed of few to tens of disclinations, in the two-stage solid-hexatic-liquid melting transition of a two-dimensional Yukawa system. We uncover the topological pathways for their formation and how the crystalline-ordered domains (CODs) with different lattice orientations nearby DCs can be formed, which affect the structural order variations in the transitions. It is found that the six basic processes: the pair generation (I), dissociation (II), scattering (III), propagation (IV), recombination (V), and pair annihilation (VI) of dislocations, each through a single bond-breaking-replacement process, govern DC evolutions. Small DCs composed of antiparallel dislocations through process I by localized particle-shear motion dominate in the solid phase. The further successive combination of processes II to IV, through successive bond-breaking-replacement rotations by stringlike cooperative hopping of several particles, are responsible for the formation of open and ring-shaped stringlike DCs composed of connected dislocations, free dislocations, free disclinations, and CODs enclosed by stringlike DCs, dominated in the hexatic phase. The spreading of neighboring small DCs or the emergence of new small DCs nearby can generate larger DCs with tens of dislocations. The combinations of reversed basic processes can break or diminish a DC. Even though the two-stage transitions can also be signified by the onsets of the rapid rises of the free disclinations and free dislocations successively, the increases of the number and averaged size of multiscale DCs enclosing CODs play the key roles for the successive losses of translational and orientational orders in the two-stage phase transitions. Published by the American Physical Society 2024

Designer pair statistics of disordered many-particle systems with novel properties.

The knowledge of exact analytical functional forms for the pair correlation function g2(r) and its corresponding structure factor S(k) of disordered many-particle systems is limited. For fundamental and practical reasons, it is highly desirable to add to the existing database of analytical functional forms for such pair statistics. Here, we design a plethora of such pair functions in direct and Fourier spaces across the first three Euclidean space dimensions that are realizable by diverse many-particle systems with varying degrees of correlated disorder across length scales, spanning a wide spectrum of hyperuniform, typical nonhyperuniform, and antihyperuniform ones. This is accomplished by utilizing an efficient inverse algorithm that determines equilibrium states with up to pair interactions at positive temperatures that precisely match targeted forms for both g2(r) and S(k). Among other results, we realize an example with the strongest hyperuniform property among known positive-temperature equilibrium states, critical-point systems (implying unusual 1D systems with phase transitions) that are not in the Ising universality class, systems that attain self-similar pair statistics under Fourier transformation, and an experimentally feasible polymer model. We show that our pair functions enable one to achieve many-particle systems with a wide range of translational order and self-diffusion coefficients D, which are inversely related to one another. One can design other realizable pair statistics via linear combinations of our functions or by applying our inverse procedure to other desirable functional forms. Our approach facilitates the inverse design of materials with desirable physical and chemical properties by tuning their pair statistics.

Surface effect on the phase separation in thin liquid crystal film as seen from a mean-field approach

The effect of the interplay between attractive nonlocal surface interactions and attractive pair long-range intermolecular couplings on molecular structures of liquid crystals confined in thin cells with flat solid surfaces has been studied. It has been shown, in the framework of the extended McMillan′s mean field theory, that in the confined LC system a complex orientational and translational ordering of molecules can be induced. Several scenarios of the formation of local smectic A, nematic, and isotropic phases have been shown to coexist in a certain temperature range. Due to the nonlocality of the surface interaction, an unexpected complexity of the spatial arrangement of these local phases along the direction of the normal to the surface may exhibit itself.

Schramm-Loewner Evolution in 2D Rigidity Percolation.

Amorphous solids may resist external deformation such as shear or compression, while they do not present any long-range translational order or symmetry at the microscopic scale. Yet, it was recently discovered that, when they become rigid, such materials acquire a high degree of symmetry hidden in the disorder fluctuations: their microstructure becomes statistically conformally invariant. In this Letter, we exploit this finding to characterize the universality class of central-force rigidity percolation (RP), using Schramm-Loewner evolution (SLE) theory. We provide numerical evidence that the interfaces of the mechanically stable structures (rigid clusters), at the rigidification transition, are consistently described by SLE_{κ}, showing that this powerful framework can be applied to a mechanical percolation transition. Using well-known relations between different SLE observables and the universal diffusion constant κ, we obtain the estimation κ∼2.9 for central-force RP. This value is consistent, through relations coming from conformal field theory, with previously measured values for the clusters' fractal dimension D_{f} and correlation length exponent ν, providing new, nontrivial relations between critical exponents for RP. These findings open the way to a fine understanding of the microstructure in other important classes of rigidity and jamming transitions.

Core-softened colloid under extreme geometrical confinement.

Geometrical constraints offer a promising strategy for assembling colloidal crystal structures that are not typically observed in bulk or under 2D conditions. Core-softened colloids, in particular, have emerged as versatile chemical building blocks with applications across various scientific and technological areas. In this study, we investigate the behavior of a core-softened model confined between two parallel walls. Employing molecular dynamics simulations, we analyze the system's response under extreme confinement, where only one or two layers of colloids are permitted. The system comprises particles modeled by a ramp-like potential confined within slit nanoslits created by two flat, purely repulsive walls with a lateral side L separated by a distance Lz. Through a systematic analysis of the phase behavior as Lz increases, or as the system undergoes decompression, for different values of L, we identified a mono-to-bilayer transition associated with changes in the colloidal structure. In the monolayer regime, we observed solid phases at lower densities than those observed in the 2D case. Importantly, we demonstrated that confinement at specific Lz values, allowing particle arrangement into two layers, can lead to the emergence of the square phase, which was not observed under monolayer or 2D conditions. By correlating thermodynamic, translational, and orientational ordering, as well as the dynamics of this confined colloidal system, our findings offer valuable insights into the utilization of geometrical constraints to induce and manipulate structural changes.

Structural building-blocks of disordered Cu-Zr alloys

The atomic structures of Cu-Zr alloys have been extensively studied due to the unusually high glass forming ability of this system. In this work, we investigate the nearest-neighbor atomic structures of several simulated disordered Cu-Zr compositions at three temperatures: 1450 K (liquid), 700 K (undercooled liquid), and 350 K (disordered solid). The results show that over 90 % of the local structures in these systems can be described by one of 12 “building-block” atomic cluster geometries, regardless of composition or temperature, and that these structures all exhibit icosahedral or quasi-icosahedral geometries. Most of the building-blocks are unique in their combination of representative Voronoi polyhedron geometry, predominant central atom type, and occupation probability for each site in the cluster. In addition to the 12 common building-blocks, 35 “outlier” structures unique to their simulated compositions and temperatures were observed. The outliers were primarily non-icosahedral. While the populations of the common building-blocks do not exhibit clear trends with temperature or composition, the overall population of outliers increased with decreasing temperature, suggestive of their role in accommodating the lack of translational order in the disordered solid.

Electric field effects on N–Sm-A–Sm-C phase transitions

A liquid crystalline system formed by rod-shaped molecules that have a small transverse dipole moment is analyzed in the presence of an external electric field normal to the smectic layers. The approach focuses on the phase transition diagram displaying the N–Sm–A-Sm-C phases, when both negative and positive dielectric anisotropies are considered. The analysis is carried out within the framework of an extended mean field theory, which shows the emergence of a re-entrant Sm-C phase in the strong field regime, accompanied by a suppression of the translational ordering of the Sm-A phase, in the case of a negative anisotropy. A different scenario is observed in the case of positive anisotropy, as the electric field tends to suppress the Sm-C phase because the molecular alignment is driven by the field along its direction. In this case, the emergence of a residual nematic phase is also observed, which replaces the isotropic phase and is characterized by a low-value orientational order parameter.

Disclinations in vibration-induced size segregation

Vibration segregates large disks embedded in a medium of small disks and transits structurally the arrays of disks from the loosely disordered packing to the densely ordered packing. Our experiments on a monodisperse or bidisperse medium of small disks reveal that several types of topological defects, emerging during this disordered-to-ordered transition, are an isolated 5-fold disclination, an isolated 7-fold disclination, a 5-7 pair, a quadrupole of two 5-7 pairs, a grain boundary of alternating 5- and 7-fold disclinations and a closed loop of a grain boundary. The dominant types are an isolated 5-fold disclination and a 5-7 pair. Vibration eliminates more effectively 5-7 pairs than isolated 5-fold disclinations. After sufficient vibration the resulting orientational order is quasi-long-range only in two cases, i) in a monodisperse medium and ii) in a dilute bidisperse medium vibrated at small acceleration, while translational order is always short-range. The arrangement of disks in such two cases is thus hexatic-like.

Self-Organization of Two-Dimensional Systems: The Role of Translational and Orientational Order Parameters

Self-Organization of Two-Dimensional Systems: The Role of Translational and Orientational Order Parameters