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We study the 1D quantum Heisenberg chain with randomly ferromagnetic or antiferromagnetic couplings [a model previously studied by approximate strong-disorder renormalization group (RG)]. We find that, at least for sufficiently large spin S, the ground state has "spin glass" order. The spin waves on top of this state have the dynamical exponent [Formula: see text], intermediate between the values z = 1 of the antiferromagnet and z = 2 of the ferromagnet. Density matrix renormalization group (DMRG) simulations are in good agreement with the analytical results for spins S = 1 and [Formula: see text]. The case [Formula: see text] shows large finite size effects: We suggest that this case is also ordered, but with a small ordered moment.

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Building a polarization center is an effective avenue to boost charge separation and molecular activation in photocatalysis. However, a limited number of polarization centers are usually created. Here, a polarization plane based on two-dimensional (2D) atomic layers is designed to maximize the surface polarization centers. The Mn in a 2D crystal lattice is etched from the MnIn2S4 atomic layers to build a consecutive symmetry-breaking structure of isolated InO1S5 sites. More charges aggregate around O, making the isolated InO1S5 sites highly polarized. Due to the formation of the InO1S5 polarization plane, an enormous polarized electric field is formed perpendicular to the 2D atomic layers and the carrier lifetime can be prolonged from 93.2 ps in MnIn2S4 to 1130 ps in amorphous MnxIn2Sy. Meantime, the formed large charge density gradient favors coupling and activation of small molecules. Benefiting from these features, a good NH3 photosynthesis performance (515.8 µmol g-1 h-1) can be realized over amorphous MnxIn2Sy, roughly 2.5 and 48.9 times higher than those of MnIn2S4 atomic layers and bulk MnIn2S4, respectively. The apparent quantum yields reach 5.4 and 3.3% at 380 and 400 nm, respectively. Meanwhile, a greatly improved CO2 reduction activity is also achieved over MnxIn2Sy. This strategy provides an accessible pathway for designing an asymmetrical polarization plane to motivate photocatalysis optimization.

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The morphological symmetry-retaining and symmetry-breaking of single crystals of the γ-cyclodextrin metal-organic framework have been achieved via introducing lower symmetric ß-cyclodextrins and α-cyclodextrins, respectively. ß-cyclodextrins led to a morphological evolution with retained symmetry from cubic to rhombic dodecahedra, while α-cyclodextrins resulted in the original cubic crystal missing a vertex angle presenting symmetry-breaking behavior. The crystal structures of rhombic dodecahedra and angle-deficient crystals were confirmed through X-ray crystallography, and the mechanisms underlying the morphological transformation evolution were further analyzed. Our work not only provides a rare case realizing two different paths of morphological evolution in one system, but also encourages future efforts towards the evolution of artificial crystal systems in a natural way.

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BACKGROUND: Mouse nodal immotile cilia mechanically sense the bending direction for left-right (L-R) determination and activate the left-side-specific signaling cascade, leading to increased Nodal activity. Asymmetric distribution of Pkd2, a crucial channel for L-R determination, on immotile cilia has been reported recently. However, the causal relationship between the asymmetric Pkd2 distribution and direction-dependent flow sensing is not well understood. Furthermore, the underlying molecular mechanism directing this asymmetric Pkd2 distribution remains unclear. RESULTS: The effects of several recombinant proteins and inhibitors on the Pkd2 distribution were analyzed using super-resolution microscopy. Notably, bone morphogenetic protein 4 (BMP4) affected the Pkd2 distribution. Additionally, three-dimensional manipulation of nodal immotile cilia using optical tweezers revealed that excess BMP4 caused defects in the mechanosensing ability of the cilia. CONCLUSIONS: Experimental data together with model calculations suggest that BMP4 regulates the asymmetric distribution of Pkd2 in nodal immotile cilia, thereby affecting the ability of these cilia to sense the bending direction for L-R determination. This study, for the first time, provides insight into the relationship between the asymmetric protein distribution in cilia and their function.

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A kagome lattice hosts a plethora of quantum states arising from the interplay between nontrivial topology and electron correlations. The recently discovered kagome magnet RMn6Sn6 (R represents a rare-earth element) is believed to showcase a kagome band closely resembling textbook characteristics. Here, we report the characterization of local electronic states and their magnetization response in YMn6Sn6 via scanning tunneling microscopy measurements under vector magnetic fields. Our spectroscopic maps reveal a spontaneously trimerized kagome electronic order in YMn6Sn6, where the 6-fold rotational symmetry is disrupted while translational symmetry is maintained. Further application of an external magnetic field demonstrates a strong coupling of the YMn6Sn6 kagome band to the field, which exhibits an energy shift discrepancy under different field directions, implying the existence of magnetization-response anisotropy and anomalous g factors. Our findings establish YMn6Sn6 as an ideal platform for investigating kagome-derived orbital magnetic moment and correlated magnetic topological states.

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Living systems at all scales are compartmentalized into interacting subsystems. This paper reviews a mechanism that drives compartmentalization in generic systems at any scale. It first discusses three symmetries of generic physical interactions in a quantum-theoretic description. It then shows that if one of these, a permutation symmetry on the inter-system boundary, is spontaneously broken, the symmetry breaking is amplified by the Free Energy Principle (FEP). It thus shows how compartmentalization generically results from permutation symmetry breaking under the FEP. It finally notes that the FEP asymptotically restores the broken symmetry, showing that the FEP can be regarded as a theory of fluctuations away from a permutation-symmetric boundary, and hence from an entangled joint state of the interacting systems.

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Stacking orders provide a unique way to tune the properties of two-dimensional materials. Recently, ABCB-stacked tetralayer graphene has been predicted to possess atypical elemental ferroelectricity arising from its symmetry breaking but has been experimentally explored very little. Here, we observe pronounced nonlinear optical second-harmonic generation (SHG) in ABCB-stacked tetralayer graphene while absent in both ABAB- and ABCA-stacked allotropes. Our results provide direct evidence of symmetry breaking in ABCB-stacked tetralayer graphene. The remarkable contrast in the SHG spectra of tetralayer graphene allows straightforward identification of ABCB domains from the other two kinds of stacking order and facilitates the characterization of their crystalline orientation. The employed SHG technique serves as a convenient tool for exploring the intriguing physics and novel nonlinear optics in ABCB-stacked graphene, where spontaneous polarization and intrinsically gapped flat bands coexist. Our results establish ABCB-stacked graphene as a unique platform for studying the rare ferroelectricity in noncentrosymmetric elemental structures.

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This study aims to investigate the impact of the π â†’ π* excitation localised in one monomer on the equilibrium geometry and oscillations of the AA dimer. Several low-frequency vibrations appear in pairs in the LIF spectrum because oscillations involving intermolecular hydrogen bonds are coupled, generating approximately symmetric and antisymmetric combinations (especially the COOH rocking modes, LIF: 295 and 301 cm-1). Furthermore, quantitative evaluation based on the TDDFT(B3LYP) results indicates that a dozen among 90 intramolecular oscillations are strongly coupled. In contrast, most vibrations are decoupled or weakly coupled, since they involve remote parts of the monomers. This makes several single vibrations active in the LIF spectrum (including the bending mode of the NH···O intramolecular hydrogen bond associated the strongest vibronic band 442 cm-1), while the other in each pair remains inactive. The reason for decoupling of oscillations and symmetry breaking is that the π â†’ π* electronic excitation is entirely localised within one of the monomers, which makes them no longer equivalent in terms of geometry and dynamics. Additionally, the excitation of one monomer induces strengthening and shortening by 6 pm of only one intermolecular hydrogen bond linking the carboxylic groups of both molecules. This causes the 1.7° in-plane distortion of the dimer and lowering of its symmetry to Cs group (from C2h for the S0 state). The distortion induces the activity of two low-frequency in-plane intermolecular vibrations, i.e. the geared oscillation (LIF: 58 cm-1) and the shearing motion (99 cm-1) of the monomers.

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Developing new approaches to fulfill the enantioseparation of nanocluster racemates and construct cluster-based nanomaterials with optical activity remains highly desired in cluster science, because it is an essential prerequisite for fundamental research and extensive applications of these nanomaterials. We herein propose a strategy termed "active-site exposing and partly re-protecting" to trigger the symmetry breaking of highly symmetrical nanoclusters and to render cluster crystals optically active. The vertex PPh3 of the symmetrical Ag29(SSR)12(PPh3)4 (SSR = 1, 3-benzenedithiol) nanocluster was firstly dissociated in the presence of counterions with large steric hindrance, and then the exposed Ag active sites of the obtained Ag29(SSR)12 nanocluster were partly re-protected by Ag+, yielding an Ag29(SSR)12-Ag2 nanocluster with a symmetry-breaking construction. Ag29(SSR)12-Ag2 followed a chiral crystallization mode, and its crystal displayed strong optical activity, derived from CD and CPL characterizations. Overall, this work presents a new approach (i.e., active-site exposing and partly re-protecting) for the symmetry breaking of highly symmetrical nanoclusters, the enantioseparation of nanocluster racemates, and the achievement of highly optical activity.

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Symmetry breaking leading to axis formation and spatial patterning is crucial for achieving more accurate recapitulation of human development in organoids. While these processes can occur spontaneously by self-organizing capabilities of pluripotent stem cells, they can often result in variation in structure and composition of cell types within organoids. To address this limitation, bioengineering techniques that utilize geometric, topological and stiffness factors are increasingly employed to enhance control and consistency. Here, we review how spontaneous manners and engineering tools such as micropattern, microfluidics, biomaterials, etc. can facilitate the process of symmetry breaking leading to germ layer patterning and the formation of anteroposterior and dorsoventral axes in blastoids, gastruloids, neuruloids and neural organoids. Furthermore, brain assembloids, which are composed of multiple brain regions through fusion processes are discussed. The overview of organoid polarization in terms of patterning tools can offer valuable insights for enhancing the physiological relevance of organoid system.

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The current bottleneck in the development of efficient photocatalysts for hydrogen evolution is the limited availability of high-performance acceptor units. Over the past nine years, dibenzo[b,d]thiophene sulfone (DBS) has been the preferred choice for the acceptor unit. Despite extensive exploration of alternative structures as potential replacements for DBS, a superior substitute remains elusive. In this study, a symmetry-breaking strategy was employed on DBS to develop a novel acceptor unit, BBTT-1SO. The asymmetric structure of BBTT-1SO proved beneficial for increasing multiple moment and polarizability. BBTT-1SO-containing polymers showed higher efficiencies for hydrogen evolution than their DBS-containing counterparts by up to 166 %. PBBTT-1SO exhibited an excellent hydrogen evolution rate (HER) of 222.03 mmol g-1 h-1 and an apparent quantum yield of 27.5 % at 500 nm. Transient spectroscopic studies indicated that the BBTT-1SO-based polymers facilitated electron polaron formation, which explains their superior HERs. PBBTT-1SO also showed 14 % higher HER in natural seawater splitting than that in deionized water splitting. Molecular dynamics simulations highlighted the enhanced water-PBBTT-1SO polymer interactions in salt-containing solutions. This study presents a pioneering example of a substitute acceptor unit for DBS in the construction of high-performance photocatalysts for hydrogen evolution.

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This Review elucidates the regulatory principles of random monoallelic expression by focusing on two well-studied examples: the X-chromosome inactivation regulator Xist and the olfactory receptor gene family. Although the choice of a single X chromosome or olfactory receptor occurs in different developmental contexts, common gene regulatory principles guide monoallelic expression in both systems. In both cases, an event breaks the symmetry between genetically and epigenetically identical copies of the gene, leading to the expression of one single random allele, stabilized through negative feedback control. Although many regulatory steps that govern the establishment and maintenance of monoallelic expression have been identified, key pieces of the puzzle are still missing. We provide an overview of the current knowledge and models for the monoallelic expression of Xist and olfactory receptors. We discuss their similarities and differences, and highlight open questions and approaches that could guide the study of other monoallelically expressed genes.

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The discovery of superconducting states in diverse topological materials generates a burgeoning interest to explore a topological superconductor and to realize a fault-tolerant topological quantum computation. A variety of routes to realize topological superconductors are proposed, and many types of topological materials are developed. However, a pristine topological material with a natural superconducting state is relatively rare as compared to topological materials with artificially induced superconductivity. Here, it is reported that the planar honeycomb structured 3D topological Dirac semimetal (TDS) SrCuBi, which is the Zintl phase, shows a natural surface superconductivity at 2.1 K under ambient pressure. It is clearly identified from theoretical calculations that a topologically nontrivial state exists on the (100) surface. Further, its superconducting transition temperature (Tc) increases by applying pressure, exhibiting a maximal Tc of 4.8 K under 6.2 GPa. It is believed that this discovery opens up a new possibility of exploring exotic Majorana fermions at the surface of 3D TDS superconductors.

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This study explores the impact of symmetry breaking on the ferromagnetic resonance of Bloch point (BP) nanospheres. Through standard Fourier analysis, we unveil two distinct oscillation mode groups characterized by low and high frequencies, respectively. Our findings emphasize the pivotal role of magnetic volume in shaping resonance amplitudes, providing new insights into the intricate dynamics of BP states. The investigation of geometric parameters reveals a quasi-monotonic decrease in resonance frequencies as a function of the asymmetry degree attributed to symmetry-breaking induced by geometric modifications. Spatial distribution analysis showcases unique resonance frequencies for the upper and lower BP hemispheres, highlighting the nuanced impact of the geometry on mode excitation. As the radius increases, additional modes emerge, demonstrating a compelling relationship between the magnetic volume and frequency. Phase analysis unveils coherent oscillations within each BP hemisphere, offering valuable insights into the rotational directions of the excitation poles. Beyond fundamental understanding, our study opens avenues for innovative applications, suggesting the potential use of nanospheres in advanced magnetic sensing, data storage, and nanoscale spintronic devices.

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Valleytronics, i.e., the manipulation of the valley degree of freedom, offers a promising path for energy-efficient electronics. One of the key milestones in this field is the room-temperature manipulation of the valley information in thick-layered material. Using scanning photocurrent microscopy, we achieve this milestone by observing a geometrically dependent circular photocurrent in a few-layer molybdenum disulfide (MoS2) under normal incidence. Such an observation shows that the system symmetry is lower than that of bulk MoS2 material, preserving the optical chirality-valley correspondence. Moreover, the circular photocurrent polarity can be reversed by applying electrical bias. We propose a model where the observed photocurrent results from the symmetry breaking and the built-in field at the electrode-sample interface. Our results show that the valley information is still retained even in thick-layered MoS2 at room temperature and opens up new opportunities for exploiting the valley index through interface engineering in multilayer valleytronics devices.

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Engineering symmetry breaking in thermoelectric materials holds promise for achieving an optimal thermoelectric efficiency. van der Waals (vdW) layered transition metal dichalcogenides (TMDCs) provide critical opportunities for manipulating the intrinsic symmetry through in-plane symmetry breaking interlayer twists and out-of-plane symmetry breaking heterostructures. Herein, the symmetry-dependent thermoelectric properties of MoS2 and MoSe2 obtained via first-principles calculations are reported, yielding an advanced ZT of 2.96 at 700 K. The underlying mechanisms reveal that the in-plane symmetry breaking results in a lowest thermal conductivity of 1.96 W·m-1·K-1. Additionally, the electric properties can be significantly modulated through band flattening and bandgap alteration, stemming directly from the modified interlayer electronic coupling strength owing to spatial repulsion effects. In addition, out-of-plane symmetry breaking induces band splitting, leading to a decrease in the degeneracy and complex band structures. Consequently, the power factor experiences a notable enhancement from ∼1.32 to 1.71 × 10-2 W·m-1·K-2, which is attributed to the intricate spatial configuration of charge densities and the resulting intensified intralayer electronic coupling. Upon simultaneous implementation of in-plane and out-of-plane symmetry breaking, the TMDCs exhibit an indirect bandgap to direct bandgap transition compared to the pristine structure. This work demonstrates an avenue for optimizing thermoelectric performance of TMDCs through the implementation of symmetry breaking.

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A symmetry-breaking in rotational spatial pattern of quasi-periodic solitary oscillations is revealed with tomography measurement of plasma emission, simultaneously with background asymmetry in stationary plasma structure. Although the oscillatory pattern deformation is a natural course in the presence of asymmetry, elaborate analyses identify existence unfeatured nonlinear effects of the background asymmetry, i.e., its nonlinear couplings with harmonic modes of rotational symmetry, to produce non-harmonic mode to break the symmetry and cause the oscillatory pattern to be chaotic. The findings suggest the unrecognized fundamental process for plasmas to be turbulent.

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External bilateral symmetry is a prevalent feature in vertebrates, which emerges during early embryonic development. To begin with, vertebrate embryos are largely radially symmetric before transitioning to bilaterally symmetry, after which, morphogenesis of various bilateral tissues (e.g somites, otic vesicle, limb bud), and structures (e.g palate, jaw) ensue. While a significant amount of work has probed the mechanisms behind symmetry breaking in the left-right axis leading to asymmetric positioning of internal organs, little is known about how bilateral tissues emerge at the same time with the same shape and size and at the same position on the two sides of the embryo. By discussing emergence of symmetry in many bilateral tissues and structures across vertebrate model systems, we highlight that understanding symmetry establishment is largely an open field, which will provide deep insights into fundamental problems in developmental biology for decades to come.

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The Dzyaloshinskii-Moriya interaction (DMI) is understood to be forbidden by the symmetry of centrosymmetric systems, thus restricting the candidate types for investigating many correlated physical phenomena. Here, we report the hidden DMI existing in centrosymmetric magnets driven by the local inversion symmetry breaking of specific spin sublattices. The opposite DMI spatially localized on the inverse spin sublattice favors the separated spin spiral with opposite chirality. Furthermore, we elucidate that hidden DMI widely exists in many potential candidates, from the first-principles calculations on the mature crystal database. Interestingly, novel topological spin configurations, such as the anti-chirality-locked merons and antiferromagnetic-ferromagnetic meron chains, are stabilized as a consequence of hidden DMI. Our understanding enables the effective control of DMI by symmetry operations at the atomic level and enlarges the range of currently useful magnets for topological magnetism.

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Kagome lattice AV3Sb5 has attracted tremendous interest because it hosts correlated and topological physics. However, an in-depth understanding of the temperature-driven electronic states in AV3Sb5 is elusive. Here we use scanning tunneling microscopy to directly capture the rotational symmetry-breaking effect in KV3Sb5. Through both topography and spectroscopic imaging of defect-free KV3Sb5, we observe a charge density wave (CDW) phase transition from an a0 × a0 atomic lattice to a robust 2a0 × 2a0 superlattice upon cooling the sample to 60 K. An individual Sb-atom vacancy in KV3Sb5 further gives rise to the local Friedel oscillation (FO), visible as periodic charge modulations in spectroscopic maps. The rotational symmetry of the FO tends to break at the temperature lower than 40 K. Moreover, the FO intensity shows an obvious competition against the intensity of the CDW. Our results reveal a tantalizing electronic nematicity in KV3Sb5, highlighting the multiorbital correlation in the kagome lattice framework.