Symmetry Breaking Process Research Articles

Polar domain walls induced by sequential symmetry breaking in frustrated mechanical metamaterials

Frustration hinders ideal local interactions in systems ranging from artificial spin ices with ice rules to mechanical metamaterials featuring regular floppy modes. While geometric frustrations have been known to promote complex ordered patterns in tessellated lattice structures, there is growing interest in global frustrations due to the topologically nontrivial geometry of metamaterials. However, multiferroic orders in globally frustrated metamaterials have remained elusive. Here, we present polar domain walls constrained in flexible mechanical metamaterials with global frustration and sequential symmetry breaking. We showcase that under simple compressive loading, competing interactions in globally frustrated metamaterials give rise to mixed deformations with high-order buckling modes described by an emergent order parameter. Utilizing an elastic mechanism model, we unveil the process of sequential symmetry breaking and capture the formation of polar domain walls exhibiting a chiral distribution within a multi-well potential landscape. We further demonstrate how to eliminate frustration through torsional loading, leading to symmetry restoration. These results provide insights into the intricate interactions between order and frustration, inspiring the modulation of domain walls in macroscopic systems.

A Goldstone boson equivalence for inflation

The effective field theory of single-field inflation characterizes the inflationary epoch in terms of a pattern of symmetry breaking. An operator acquires a time-dependent vacuum expectation value, defining a preferred spatial slicing. In the absence of dynamical gravity, the fluctuations around the time-dependent background are described by the Goldstone boson associated with this symmetry breaking process. With gravity, the Goldstone is eaten by the metric, becoming the scalar metric fluctuation. In this paper, we will show that in general single-field inflation, the statistics of scalar metric fluctuations are given by the statistics of this Goldstone boson decoupled from gravity up to corrections that are controlled as an expansion in slow-roll parameters. This even holds in the presence of additional parameters, like the speed of sound, that naively enhance the impact of the gravitational terms. In the process, we derive expressions for leading and sub-leading gravitational corrections to all-orders in the Goldstone boson.

Reduction of turbulence by enhanced low-frequency zonal flow-like structures in HL-2A edge plasmas

Abstract A low-frequency zonal flow-like (LFZF-like) structure peaking at f ≈ 2.0 kHz has been observed in HL-2A ohmically heated deuterium plasmas using a combined Langmuir probe array. This time-varying potential structure, which has axisymmetric characteristics (n = 0) and a finite radial correlation length (less than 1 cm), was identified to be generated by the three-wave interaction in small-scale turbulence. The results illustrate that the amplitude of the LFZF-like structure dramatically increases with the influence of impurity ions, which is mainly due to the increased strength in the nonlinear energy transfer by the turbulence vortex symmetry-breaking process. Consequently, the enhanced LFZF-like structure has the ability to stabilize the local turbulence via the shearing decorrelation mechanism as demonstrated in this experiment. The observed results given here reveal the essential role played by the LFZF-like structure in the reduction of turbulence levels, which could advance our understanding of the multi-scale physics governing turbulence and the resulting transport in magnetically confined plasmas.

Coupled Kite-to-Square Distortion Transition and Physical Properties in 2D Lead Halide Perovskite.

2D lead halide perovskites showcase diverse electrical and optoelectrical properties due to their adaptable structural distortion, which dictates the symmetry characteristics of the material. To accommodate the geometric shape of the cation, the inorganic layer of the 2D perovskite often undergoes specific distortions such as lead-halide bond length elongation/compression and lead atom displacement. The resultant distortion manifests as a quadrilateral shape formed by Pb atoms from four adjacent four octahedrons. The degree of distortion increases as the quadrilateral deviates further from a square shape and vice versa. This quadrilateral shape not only visually represents the magnitude of distortion but also confirms its direction. During the transition from kite to square distortion under external stimuli, the positions of the Pb atoms vividly illustrate the symmetry-breaking process, corresponding to a shift from high to low symmetry states. The electrical and optoelectronic properties, including ferroelectricity, pyroelectricity, piezoelectricity, nonlinear optical properties, and characteristics related to bulky photovoltaic effects, some of them exhibit direction dependence nature. This perspective employed a visible structural distortion approach to elucidate symmetry breaking and coupling distortion transitions with eight optoelectronic physical properties in 2D layered perovskite. We review recent research advancements and outline current challenges that help us to understand the structure-property relationship of 2D perovskite.

Patterning and folding of intestinal villi by active mesenchymal dewetting

Tissue folds are structural motifs critical to organ function. In the intestine, bending of a flat epithelium into a periodic pattern of folds gives rise to villi, finger-like protrusions that enable nutrient absorption. However, the molecular and mechanical processes driving villus morphogenesis remain unclear. Here, we identify an active mechanical mechanism that simultaneously patterns and folds the intestinal epithelium to initiate villus formation. At the cellular level, we find that PDGFRA+ subepithelial mesenchymal cells generate myosin II-dependent forces sufficient to produce patterned curvature in neighboring tissue interfaces. This symmetry-breaking process requires altered cell and extracellular matrix interactions that are enabled by matrix metalloproteinase-mediated tissue fluidization. Computational models, together with invitro and invivo experiments, revealed that these cellular features manifest at the tissue level as differences in interfacial tensions that promote mesenchymal aggregation and interface bending through a process analogous to the active dewetting of a thin liquid film.

Breaking of Lateral Symmetry in Two-Dimensional Crystallization-Driven Self-Assembly on a Surface.

Symmetry breaking is prevalent in nature and provides distinctive access to hierarchical structures for artificial materials. However, it is rarely explored in two-dimensional (2D) entities, especially for lateral asymmetry. Herein, we describe a unique symmetry breaking process in surface-initiated 2D living crystallization-driven self-assembly. The 2D epitaxial growth occurs only at one lateral side of the immobilized cylindrical micelle seeds, accessing unilateral platelets with the yield increasing with the seed length, the growth temperature, and poly(2-vinylpyridine) corona length (maximum = 92%). Generally, the tilted immobilization of seeds blocks one lateral side and triggers the lateral symmetry breaking, where the intensity and spatial arrangement of seed-surface interactions dictate the regulation. Segmented unilateral platelets with segmented corona regions are further fabricated with the addition of different blended unimers. Remarkably, discrete slope-like and dense blade-like platelet arrays grow off the surface when seeds are compactly aligned either with spherical micelles or themselves. This strategy provides nanoscale insights into the symmetry breaking in long-range self-assembly and would be promising for the design of innovative colloids and smart surfaces.

Dissipative Structures and Self-Organization Process in an Abstract Model of Neural Network

This preliminary study shows an abstract model of the learning process; it will be identified as creating a dissipative structure and forming a self-organization process.The dissipative structure will provoke a correlation within the whole system using the associated symmetry-breaking process.

Symmetry breaking and chiral amplification in prebiotic ligation reactions.

The single chirality of biological molecules is a signature of life. Yet, rationalizing how single chirality emerged remains a challenging goal1. Research has commonly focused on initial symmetry breaking and subsequent enantioenrichment of monomer building blocks-sugars and amino acids-that compose the genetic polymers RNAand DNA as well as peptides. If these building blocks are only partially enantioenriched, however, stalling of chain growth may occur, whimsically termed in the case of nucleic acids as "the problem of original syn"2. Here, in studying a new prebiotically plausible route to proteinogenic peptides3-5, we discovered that the reaction favours heterochiral ligation (that is, the ligation of L monomers with D monomers). Although this finding seems problematic for the prebiotic emergence of homochiral L-peptides, we demonstrate, paradoxically, that this heterochiral preference provides a mechanism for enantioenrichment in homochiral chains. Symmetry breaking, chiral amplification and chirality transfer processes occur for all reactants and products in multicomponent competitive reactions even when only one of the molecules in the complex mixture exhibits an imbalance in enantiomer concentrations (non-racemic). Solubility considerations rationalizefurther chemical purification and enhanced chiral amplification. Experimental data and kinetic modelling support this prebiotically plausible mechanism for the emergence of homochiral biological polymers.

Coupling-induced bistability in self-oscillating regimes of two coupled identical Spin-Torque Nano-oscillators

We consider a system of two coupled identical Spin Torque Nano-Oscillators (STNOs) with cylindrical geometry. The STNOs have free layers in the vortex magnetization configuration and fixed layer with magnetization in the out-of-plane direction. The magnetization dynamics in the two STNOs are analyzed by using a Thiele-like equation governing the dynamics of the vortex core positions. The coupling is assumed to be linear and symmetric and this enables to characterize it by a single complex parameter. We consider numerical simulations of the model as a function of the coupling strength k and phase ϕk. Depending on their values, different motions of the vortex cores are observed, e.g. periodic, and quasi-periodic. Each type of dynamics can be classified according to the symmetry property shown by the trajectories. In this respect, the transition between different types of motion corresponds to a symmetry-breaking process and we describe it as a bifurcation process. Fixing the value of the coupling constant phase, we found that there is a range of coupling constant strength in which the periodic and quasi-periodic motions coexist and both are stable. This bistability is an interesting phenomenon in connection to research on neuromorphic circuits based on STNOs.

V-Shaped Tröger Oligothiophenes Boost Triplet Formation by CT Mediation and Symmetry Breaking.

A new family of molecules obtained by coupling Tröger's base unit with dicyanovinylene-terminated oligothiophenes of different lengths has been synthesized and characterized by steady-state stationary and transient time-resolved spectroscopies. Quantum chemical calculations allow us to interpret and recognize the properties of the stationary excited states as well as the time-dependent mechanisms of singlet-to-triplet coupling. The presence of the diazocine unit in Tröger's base derivatives is key to efficiently producing singlet-to-triplet intersystem crossing mediated by the role of the nitrogen atoms and of the almost orthogonal disposition of the two thiophene arms. Spin-orbit coupling-mediated interstate intersystem crossing (ISC) is activated by a symmetry-breaking process in the first singlet excited state with partial charge transfer character. This mechanism is a characteristic of these molecular triads since the independent dicyanovinylene-oligothiophene branches do not display appreciable ISC. These results show how Tröger's base coupling of organic chromophores can be used to improve the ISC efficiency and tune their photophysics.

Engineering the fracture resistance of 2H-transition metal dichalcogenides using vacancies: An in-silico investigation based on HRTEM images

Vacancy engineering of 2H-transition metal dichalcogenides (2H-TMDs) has recently attracted great attention due to its potential to fine-tune the phonon and opto-electric properties of these materials. From a mechanical perspective, this symmetry-breaking process typically reduces the overall crack resistance of the material and adversely affects its reliability. However, vacancies can trigger the formation of heterogeneous phases that synergistically improve fracture properties. In this study, using MoSe2 as an example, we characterize the types and density of vacancies that can emerge under electron irradiation and quantify their effect on fracture. Molecular dynamic (MD) simulations, employing a re-parameterized Tersoff potential capable of accurately capturing bond dissociation and structural phase changes, reveal that isolated transition metal monovacancies or chalcogenide divacancies tend to arrest the crack tip and hence enhance the monolayer toughness. In contrast, isolated chalcogenide monovacancies do not significantly affect toughness. The investigation further reveals that selenium vacancy lines, formed by high electron dose rates, alter the crack propagating direction and lead to multiple crack kinking. Using atomic displacements and virial stresses together with a continuum mapping, displacement, strain, and stress fields are computed to extract mechanistic information, e.g., conditions for crack kinking and size effects in fracture events. The study also reveals the potential of specific defect patterns, “vacancy engineering,” to improve the toughness of 2H-TMDs materials.

Probing the electroweak symmetry breaking history with gravitational waves

We perform three dimensional lattice simulation of the electroweak symmetry breaking process through two-step vacuum-like phase transitions with one step being first-order. Our results show that: 1) when the electroweak symmetry breaking is driven by the beyond Standard Model theories through the Higgs-portal, the gravitational wave spectra produced from the phase transitions are of broken power-law shape; 2) when the electroweak symmetry breaking is induced by a first-order phase transition of a high-scale theory respecting the global U(1) symmetry, cosmic strings can form and then decay through particle radiation. The two scenarios can be distinguished through probing the stochastic gravitational wave backgrounds. Our study suggests that the stochastic gravitational wave backgrounds provide an alternative way to probe the beyond Standard Model theories relevant to the electroweak symmetry breaking in the early Universe.

Time space and single-cell resolved tissue lineage trajectories and laterality of body plan at gastrulation

Understanding of the molecular drivers of lineage diversification and tissue patterning during primary germ layer development requires in-depth knowledge of the dynamic molecular trajectories of cell lineages across a series of developmental stages of gastrulation. Through computational modeling, we constructed at single-cell resolution, a spatio-temporal transcriptome of cell populations in the germ-layers of gastrula-stage mouse embryos. This molecular atlas enables the inference of molecular network activity underpinning the specification and differentiation of the germ-layer tissue lineages. Heterogeneity analysis of cellular composition at defined positions in the epiblast revealed progressive diversification of cell types. The single-cell transcriptome revealed an enhanced BMP signaling activity in the right-side mesoderm of late-gastrulation embryo. Perturbation of asymmetric BMP signaling activity at late gastrulation led to randomization of left-right molecular asymmetry in the lateral mesoderm of early-somite-stage embryo. These findings indicate the asymmetric BMP activity during gastrulation may be critical for the symmetry breaking process.

Fluid extraction from the left-right organizer uncovers mechanical properties needed for symmetry breaking.

Humans and other vertebrates define body axis left-right asymmetry in the early stages of embryo development. The mechanism behind left-right establishment is not fully understood. Symmetry breaking occurs in a dedicated organ called the left-right organizer (LRO) and involves motile cilia generating fluid-flow therein. However, it has been a matter of debate whether the process of symmetry breaking relies on a chemosensory or a mechanosensory mechanism (Shinohara et al., 2012). Novel tailored manipulations for LRO fluid extraction in living zebrafish embryos allowed us to pinpoint a physiological developmental period for breaking left-right symmetry during development. The shortest critical time-window was narrowed to one hour and characterized by a mild counterclockwise flow. The experimental challenge consisted in emptying the LRO of its fluid, abrogating simultaneously flow force and chemical determinants. Our findings revealed an unprecedented recovery capacity of the embryo to re-fil and re-circulate new LRO fluid. The embryos that later developed laterality problems were found to be those that had lower anterior angular velocity and thus less anterior-posterior heterogeneity. Next, aiming to test the presence of any secreted determinant, we replaced the extracted LRO fluid by a physiological buffer. Despite some transitory flow homogenization, laterality defects were absent unless viscosity was altered, demonstrating that symmetry breaking does not depend on the nature of the fluid content but is rather sensitive to fluid mechanics. Altogether, we conclude that the zebrafish LRO is more sensitive to fluid dynamics for symmetry breaking.

Robust negative longitudinal magnetoresistance and spin–orbit torque in sputtered Pt3Sn and Pt3SnxFe1-x topological semimetal

Contrary to topological insulators, topological semimetals possess a nontrivial chiral anomaly that leads to negative magnetoresistance and are hosts to both conductive bulk states and topological surface states with intriguing transport properties for spintronics. Here, we fabricate highly-ordered metallic Pt3Sn and Pt3SnxFe1-x thin films via sputtering technology. Systematic angular dependence (both in-plane and out-of-plane) study of magnetoresistance presents surprisingly robust quadratic and linear negative longitudinal magnetoresistance features for Pt3Sn and Pt3SnxFe1-x, respectively. We attribute the anomalous negative longitudinal magnetoresistance to the type-II Dirac semimetal phase (pristine Pt3Sn) and/or the formation of tunable Weyl semimetal phases through symmetry breaking processes, such as magnetic-atom doping, as confirmed by first-principles calculations. Furthermore, Pt3Sn and Pt3SnxFe1-x show the promising performance for facilitating the development of advanced spin-orbit torque devices. These results extend our understanding of chiral anomaly of topological semimetals and can pave the way for exploring novel topological materials for spintronic devices.

Learning Complexity to Guide Light-Induced Self-Organized Nanopatterns.

Ultrafast laser irradiation can induce spontaneous self-organization of surfaces into dissipative structures with nanoscale reliefs. These surface patterns emerge from symmetry-breaking dynamical processes that occur in Rayleigh-Bénard-like instabilities. In this study, we demonstrate that the coexistence and competition between surface patterns of different symmetries in two dimensions can be numerically unraveled using the stochastic generalized Swift-Hohenberg model. We originally propose a deep convolutional network to identify and learn the dominant modes that stabilize for a given bifurcation and quadratic model coefficients. The model is scale-invariant and has been calibrated on microscopy measurements using a physics-guided machine learning strategy. Our approach enables the identification of experimental irradiation conditions for a desired self-organization pattern. It can be generally applied to predict structure formation in situations where the underlying physics can be approximately described by a self-organization process and data is sparse and nontime series. Our Letter paves the way for supervised local manipulation of matter using timely controlled optical fields in laser manufacturing.

Microtubule detyrosination drives symmetry breaking to polarize cells for directed cell migration

To initiate directed movement, cells must become polarized, establishing a protrusive leading edge and a contractile trailing edge. This symmetry-breaking process involves reorganization of cytoskeleton and asymmetric distribution of regulatory molecules. However, what triggers and maintains this asymmetry during cell migration remains largely elusive. Here, we established a micropatterning-based 1D motility assay to investigate the molecular basis of symmetry breaking required for directed cell migration. We show that microtubule (MT) detyrosination drives cell polarization by directing kinesin-1-based transport of the adenomatous polyposis coli (APC) protein to cortical sites. This is essential for the formation of cell's leading edge during 1D and 3D cell migration. These data, combined with biophysical modeling, unveil a key role for MT detyrosination in the generation of a positive feedback loop linking MT dynamics and kinesin-1-based transport. Thus, symmetry breaking during cell polarization relies on a feedback loop driven by MT detyrosination that supports directed cell migration.

Asymmetric dark matter with a spontaneously broken U(1)′ : Self-interaction and gravitational waves

Motivated by the collisionless cold dark matter small scale structure problem, we propose an asymmetric dark matter model where dark matter particle interact with each other via a massive dark gauge boson. This model easily avoid the strong limits from cosmic microwave background (CMB) observation, and have a large parameter space to be consistent with small scale structure data. We focus on a special scenario where portals between dark sector and visible sector are too weak to be detected by traditional methods. We find that this scenario can increase the effective number of neutrinos ($N_{\text{eff}}$).In addition, the spontaneous $U(1)'$ symmetry breaking process, which makes dark gauge boson massive, can generate stochastic gravitational waves with peak frequency around $10^{-6} - 10^{-7} \text{ Hz}$.

In situ study of chiral symmetry breaking in sodium chlorate solutions by Mueller matrix polarimetry.

This work presents a novel approach for investigating symmetry-breaking processes during crystallization using Mueller matrix polarimetry. By applying this method to the cooling process of NaClO3 solutions, we demonstrate its ability to capture not only the initial and final stages of crystallization but also the intermediate steps and dynamics of the process. This technique provides more comprehensive information and insights into the symmetry-breaking mechanisms involved in crystal formation. Overall, this study highlights the potential of Mueller matrix polarimetry for in situ statistical measurements of the optical rotation and for monitoring the evolution of enantiomeric excesses.

Molecular mechanism of core planar cell polarity complex function elucidated with single-molecule methods.

The planar cell polarity (PCP) signaling pathway polarizes epithelial cells along an axis parallel to the epithelial sheet in order to generate front-back asymmetry at the tissue level. Failures in PCP signaling underlie developmental defects and diseases such as neural tube and heart defects, deafness and contribute to cancer. Six core PCP proteins assemble into large, asymmetric complexes at cell-cell junctions, with Vang and Prickle recruited to one side of the cell-cell junction while Frizzled and Dishevelled are recruited to the other. How this asymmetric assembly process occurs is not known. Genetic evidence suggests that the process of symmetry breaking at PCP clusters is coupled to cluster formation. To test how this occurs, we developed a method to count the number of each of the six core proteins in individual PCP complexes. Specifically, by analyzing bleaching traces obtained with a high frame rate in live Drosophila wing cells imaged using total internal reflection microscopy, we quantify the intensity of single fluorophores in each complex and thereby calculate the molecular number in the corresponding PCP complex. Using this approach, we find that the molecular size distribution of PCP complexes follows an exponential function, indicating a single underlying growth mechanism. We report that specifically, the number of Vang molecules in PCP complexes increases from 15 hours after puparium formation until reaching a steady state around 28 hours. Besides, we measure the asymmetry as a function of cluster size and test the dependence of the observed relationship by introducing gain and loss of function mutations that perturb cluster assembly. In conclusion, our findings provide a detailed understanding of how the PCP mechanism generates stable polarization during embryonic development.