Symmetry Breaking Research Articles

Kohn-Sham inversion for open-shell systems.

Methods based on density-functional theory usually treat open-shell atoms and molecules within the spin-unrestricted Kohn-Sham (KS) formalism, which breaks symmetries in real and spin space. Symmetry breaking is possible because the KS Hamiltonian operator does not need to exhibit the full symmetry of the physical Hamiltonian operator, but only the symmetry of the spin density, which is generally lower. Symmetry breaking leads to spin contamination and prevents a proper classification of the KS wave function with respect to the symmetries of the physical electron system. Formally well-justified variants of the KS formalism that restore symmetries in real space, in spin space, or in both have been introduced long ago, but have rarely been used in practice. Here, we introduce numerically stable KS inversion methods to construct reference KS potentials from reference spin-densities for all four possibilities to treat open shell systems, non-symmetrized, spin-symmetrized, space-symmetrized, and fully-symmetrized. The reference spin-densities are obtained by full configuration interaction and high-level coupled cluster methods for the considered atoms and diatomic molecules. The decomposition of the total energy in contributions such as the non-interacting kinetic, the exchange, and the correlation energy is different in the four KS formalisms. Reference values for these differences are provided for the considered atoms and molecules. All KS inversions, except the fully symmetrized one, lead in some cases to solutions violating the Aufbau principle. In the purely spin-symmetrized KS formalism, this represents a violation of the KS v-representability condition, i.e., no proper KS wave functions exist in those cases.

High transmission in 120-degree sharp bends of inversion-symmetric and inversion-asymmetric photonic crystal waveguides

Bending loss is one of the serious problems for constructing nanophotonic integrated circuits. Recently, many works reported that valley photonic crystals (VPhCs) enable significantly high transmission via 120-degree sharp bends. However, it is unclear whether the high bend-transmission results directly from the valley-photonic effects, which are based on the breaking of inversion symmetry. In this study, we conduct a series of comparative numerical and experimental investigations of bend-transmission in various triangular PhCs with and without inversion symmetry and reveal that the high bend-transmission is solely determined by the domain-wall configuration and independent of the existence of the inversion symmetry. Preliminary analysis of the polarization distribution indicates that high bend-transmissions are closely related to the appearance of local topological polarization singularities near the bending section. Our work demonstrates that high transmission can be achieved in a much wider family of PhC waveguides, which may provide novel designs for low-loss nanophotonic integrated circuits with enhanced flexibility and a new understanding of the nature of valley-photonics.

Integrated optical switches based on Kerr symmetry breaking in microresonators

With the rapid development of the Internet of Things and big data, integrated optical switches are gaining prominence for applications in on-chip optical computing, optical memories, and optical communications. Here, we propose a novel approach for on-chip optical switches by utilizing the nonlinear optical Kerr effect induced spontaneous symmetry breaking (SSB), which leads to two distinct states of counterpropagating light in ring resonators. This technique is based on our first experimental observation of on-chip symmetry breaking in a high-Q (9.4×106) silicon nitride resonator with a measured SSB threshold power of approximately 3.9 mW. We further explore the influence of varying pump powers and frequency detunings on the performance of SSB-induced optical switches. Our work provides insights into the development of new types of photonic data processing devices and provides an innovative approach for the future implementation of on-chip optical memories.

Effect of Exact Exchange on the Energy Landscape in Self-Consistent Field Theory.

Density functional approximations can reduce the spin symmetry breaking observed for self-consistent field (SCF) solutions compared to Hartree-Fock theory, but the amount of exact Hartree-Fock (HF) exchange appears to be a key determinant in broken Ŝ2 symmetry. To elucidate the precise role of exact exchange, we investigate the energy landscape of unrestricted Hartree-Fock and Kohn-Sham density functional theory for benzene and square cyclobutadiene, which provide paradigmatic examples of closed-shell and open-shell electronic structures, respectively. We find that increasing the amount of exact exchange leads to more local SCF minima, which can be characterized as combinatorial arrangements of unpaired electrons in the carbon π system. Furthermore, we studied the pathways connecting local minima to understand the relationships between different solutions. Our analysis reveals a subtle balance between one- and two-body interactions in determining SCF symmetry breaking, shedding new light on the physical driving forces for spin-symmetry-broken solutions in SCF approaches.

Symmetry Breaking as a Basis for Characterization of Dielectric Materials

This paper introduces a novel method for measuring the dielectric permittivity of materials within the microwave and millimeter wave frequency ranges. The proposed approach, classified as a guided wave transmission system, employs a periodic transmission line structure characterized by mirror/glide symmetry. The dielectric permittivity is deduced by measuring the transmission properties of such structure when presence of the dielectric material breaks the inherent symmetry of the structure and consequently introduce a stopband in propagation characteristic. To explore the influence of symmetry breaking on propagation properties, an analytical dispersion equation, for both symmetries, is formulated using the Rigorous Coupled Wave Analysis (RCWA) combined with the matrix transverse resonance condition. Based on the analytical equation, an optimization procedure and linearized model for a sensing structure is obtained, specifically for X-band characterization of FR4 substrates. The theoretical results of the model are validated with full wave simulations and experimentally.

Observation of broadband super-absorption of electromagnetic waves through space-time symmetry breaking.

Using time as an additional design parameter in electromagnetism, photonics, and wave physics is attracting considerable research interest, motivated by the possibility to explore physical phenomena and engineering opportunities beyond the limits of time-invariant systems. Here, we report the experimental demonstration of enhanced broadband absorption of electromagnetic waves in a continuously modulated time-varying system, exceeding one of the key theoretical limits of linear time-invariant absorbers. This is achieved by harnessing the frequency-wave vector transitions and enhanced interference effects enabled by breaking both continuous space- and time-translation symmetries in a periodically time-modulated absorbing structure operating at radio frequencies. Furthermore, we demonstrate broadband coherent wave absorption using a secondary control wave, observing a nearly perfect, reconfigurable, antireflection effect over a broad continuous bandwidth. Our findings provide insights into enhanced wave absorption in time-varying scenarios and may enable the development of devices operating in a regime fundamentally beyond the reach of linear time-invariant systems.

Promising mechanical, electronic and piezoelectric properties of grapheneplus-like BCN monolayer: insights from first-principles.

Two-dimensional (2D) carbon allotropes, together with their binary and ternary counterparts, have attracted substantial research interest due to their peculiar geometries and properties. Among them, grapheneplus, a derivative of penta-graphene, has been proposed to exhibit unusual mechanical and electronic behaviour. In this work, we perform a comprehensive first-principles study on its isoelectronic and isostructural analogue, a grapheneplus-like BCN (gp-BCN) monolayer. It is found that this gp-BCN system exhibits robust structural stability from energetic, dynamic, thermal, and mechanical perspectives. A remarkable anisotropy is observed in its mechanical behaviour, which even presents in-plane auxeticity with a high negative Poisson's ratio of -0.3. Different from the semimetallic grapheneplus one, the gp-BCN monolayer is a semiconductor with a direct band gap of 3.23 eV. High electron mobilities up to 103 cm2 V-1 s-1 appear in the gp-BCN system, which are one to two orders of magnitude greater than the hole mobilities. Furthermore, due to the breaking of inversion symmetry, the gp-BCN monolayer exhibits spontaneous out-of-plane polarization, yielding prominent out-of-plane piezoelectric responses that are comparable to those of Janus MoSSe, WSSe and H-decorated BN systems. Our study demonstrates that the BCN analogue of grapheneplus possesses promising mechanical, electronic, and piezoelectric properties, rendering it promising for applications in nanoelectronics and mechanical nanosensors.

Generalizing measurement-induced phase transitions to information exchange symmetry breaking

Generalizing measurement-induced phase transitions to information exchange symmetry breaking

QCD axion strings or seeds?

We study the impact of QCD axion strings on the cosmological history of electroweak (EW) symmetry breaking, focussing on the minimal KSVZ axion model. We consider the case of the pure SM Higgs potential as well as a simple scenario with a first order EW phase transition. We capture the effect of the Peccei-Quinn (PQ) sector within an effective-theory approach for the Higgs field, where the axion string core and the heavy PQ states are integrated out. The relevant parameters in this effective theory are controlled by the size of the portal coupling between the Higgs and the PQ scalar, and the mass of the PQ radial excitation. We determine the range of portal couplings for which the axion strings can strongly affect the dynamics of EW symmetry breaking. In the case of a first order EW phase transition, the strings can act as seeds by either catalyzing the nucleation of (non-spherical) bubbles, or leading to the completion of the phase transition by triggering a classical instability.

Electroweak phase transition in two scalar singlet model with pNGB dark matter

We investigate the dynamics of the electroweak phase transition within an extended Standard Model framework that includes one real scalar (Φ) and one complex scalar (S), both of which are SM gauge singlets. The global U(1) symmetry is softly broken to a Z3 symmetry by the S3 term in the scalar potential. After this U(1) symmetry breaking, the imaginary component of the complex scalar (S) acts as a pseudo-Nambu-Goldstone boson (pNGB) dark matter candidate, naturally stabilized by the Z2 symmetry of the scenario. Specially, the spontaneous breaking of the global U(1) symmetry to a discrete Z3 subgroup can introduce effective cubic terms in the scalar potential, which facilitates a strong first-order phase transition. We analyze both single-step and multi-step first-order phase transitions, identifying the parameter space that satisfies the dark matter relic density constraints, complies with all relevant experimental constraints, and exhibits a strong first-order electroweak phase transition. The interplay of these criteria significantly restricts the model parameter space, often leading to an underabundant relic density. Moreover, we delve into the gravitational wave signatures associated with this framework, offering valuable insights that complement traditional dark matter direct and indirect detection methods.

Regulative Fe‐3d Orbitals via Lying‐Down Conformation of Metalorganic Molecules‐Axially Coordinated MXene for Rechargeable Zn–Air Batteries

AbstractA bifunctional electrocatalyst is developed, exhibiting high catalytic activity and reversibility for the oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) through a regulative Fe d‐orbital engineering strategy. In this strategy, iron phthalocyanine organic molecule (FeOM) crystals are axially coordinated onto multilayer Mo2CTx MXene (FeOM‐Mo2CTx), adopting a lying‐down conformation. This hybridization fosters unique electronic guest–host interactions, with FeOM donating charge to Mo2CTx via Fe−O bonding, leading to symmetry breaking in electronic distribution and modified delocalization of Fe‐3d charge, accompanied by a Fe(II) spin‐state transition. These transformations enhance the adsorption and desorption toward oxygenated intermediates, optimizing the *OOH−*O transition to boost the reversibility of ORR and OER kinetics. The FeOM‐Mo2CTx exhibits a favorable ORR half‐wave potential of 0.961 V and a minimal OER overpotential of 349 mV at 10 mA cm−2 in 1.0 m KOH. The assembled aqueous zinc‐air battery (ZAB) achieves a peak power density of 155.3 mW cm−2 and exceptional charge–discharge durability over 1500 h, outperforming a conventional (Pt/C + RuO2) system. Overall, the findings underscore the significance of electronic structural engineering of FeOM with Mo2CTx, paving the way for innovative air cathodes in the development of rechargeable ZABs with enhanced performance and cost‐effectiveness.

Elongator is a microtubule polymerase selective for polyglutamylated tubulin.

Elongator is a tRNA-modifying complex that regulates protein translation. Recently, a moonlighting function of Elongator has been identified in regulating the polarization of the microtubule cytoskeleton during asymmetric cell division. Elongator induces symmetry breaking of the anaphase midzone by selectively stabilizing microtubules on one side of the spindle, contributing to the downstream polarized segregation of cell-fate determinants, and therefore to cell fate determination. Here, we investigate how Elongator controls microtubule dynamics. Elongator binds both to the tip of microtubules and to free GTP-tubulin heterodimers using two different subcomplexes, Elp123 and Elp456, respectively. We show that these activities must be coupled for Elongator to decrease the tubulin critical concentration for microtubule elongation. As a consequence, Elongator increases the growth speed and decreases the catastrophe rate of microtubules. Surprisingly, the Elp456 subcomplex binds to tubulin tails and has strong selectivity towards polyglutamylated tubulin. Hence, microtubules assembled by Elongator become selectively enriched with polyglutamylated tubulin, as observed in vitro, in mouse and Drosophila cell lines, as well as in vivo in Drosophila Sensory Organ Precursor cells. Therefore, Elongator rewrites the tubulin code of growing microtubules, placing it at the core of cytoskeletal dynamics and polarization during asymmetric cell division.

SymmPi: Exploiting Symmetry Removal for Fast Subgraph Matching

Abstract Symmetry, a phenomenon of self-similarity, is common in many networks, which often incurs a lot of redundant accesses and computations, even duplicate results when executing graph matching tasks. Many approaches (e.g. symmetry-breaking methods) try to disrupt symmetry by translating symmetry into restrictions and then imposing restrictions on the exploration order. However, the restrictions are finer-grained. If the pattern graph is complex, more restrictions are generated from symmetry breaking methods, thus complicating the exploration process and degrading the performance. Here, we present novel SymmPi, which exploits symmetry removal for fast graph matching. SymmPi first identifies the coarse-grained axisymmetric subgraphs of the given pattern graphs instead of finer relationships. If a pattern graph is not axisymmetric, SymmPi will remove some of its edges until axisymmetric subgraphs are found. Thus, the original pattern graph is transformed to a set of axisymmetric subgraphs plus some edges. Then, SymmPi finds the matches of the axisymmetric subgraph and extends these matches to the original pattern graphs by permuting the matches with additional checks. Our experiments on both directed and undirected graphs, demonstrate that SymmPi achieves a significant performance improvement over the state-of-the-art undirected and directed graph matching methods and systems.

Trans-scale live-imaging of an E5.5 mouse embryo using incubator-type biaxial light-sheet microscopy.

During mouse embryonic development, the embryonic day (E) 5.5 stage represents a crucial period for the formation of the primitive body axis, where the symmetry breaking of cellular states influences the multicellular system. Elucidating the detailed mechanisms of this process necessitates a trans-layered dynamic observation of the embryo and all internal cells. In this report, we present our success in achieving in-toto single-cell observation in a whole hemisphere of an E5.5 embryo for 12 h, using a newly developed incubator-type biaxial light-sheet microscope. To achieve the success, we optimized our microscope system, including an incubator for culture stability, and refining the observation protocol to reduce phototoxicity. Our key discovery is that the scan speed during light-sheet formation plays a critical role in reducing phototoxicity, rather than the irradiation intensity or the interval time between frames. This innovative system not only enabled in-toto single-cell tracking but also led to the discovery of the abrupt shrinking of embryos whose contractile center was located at the extraembryonic ectoderm during monotonous growth up to the E6.5 stage.

Electric Field-Induced Nonreciprocal Directional Dichroism in a Time-Reversal-Odd Antiferromagnet.

Antiferromagnets with broken time-reversal ( ) symmetry ( -odd antiferromagnets) have gained extensive attention, mainly due to their ferromagnet-like behavior despite the absence of net magnetization. However, certain types of -odd antiferromagnets remain inaccessible by the typical ferromagnet-like phenomena (e.g., anomalous Hall effect). One such system is characterized by a -odd scalar quantity, the magnetic toroidal monopole. To access the broken symmetry in such a system, a unique nonreciprocal optical phenomenon, electric field-induced nonreciprocal directional dichroism (E-induced NDD), is employed. Signals of E-induced NDD are successfully detected in a -odd antiferromagnet, Co₂SiO₄, whose magnetic structure is characterized by the magnetic toroidal monopole. Furthermore, by spatially resolving the E-induced NDD, spatial distributions of a pair of domain states related to one another by the operation are visualized. The domain imaging revealed the inversion of the domain pattern by applying a magnetic field, which is explained by trilinear coupling attributed to the piezomagnetic effect. The observation of E-induced NDD highlights unique functionalities of -odd antiferromagnets.

Broken Symmetry and Elastic Frustration in Isostructural Spin Crossover Crystals.

Symmetry-breaking spin-state transitions in two of three isostructural salts of MnIII spin-crossover cations, [MnIII(3-OMe-5-NO2-sal2323)]+, with heavy anions are reported. The ReO4- salt undergoes two-step spin crossover which is coupled with a re-entrant symmetry-breaking structural phase transition between a high temperature phase (S = 2, C2/c), an intermediate ordered phase (S = 1/S = 2, P21/c), and a low temperature phase (S = 1, C2/c). The AsF6- complex undergoes an abrupt transition between a high temperature phase (S = 2, C2/c) and a low temperature ordered phase (S = 1/S = 2, P-1). The SbF6- complex undergoes a gradual transition between a high temperature phase (S = 2, P-1) and a low temperature spin-state ordered phase (S = 1/S = 2, P-1). Correlation of the volume of the anion andT1/2in these complexes and three analogous complexes with similar anions, BF4-, ClO4-, PF6-, reveals an increase in T1/2 upon increasing the anion volume. We rationalise that the volume of the anionsmodulates the elastic interactions between the MnIII sites, with increasing elastic frustration with the larger anions resulting in a two-stepped transition for [MnIII(3-OMe-5-NO2-sal2323)]ReO4and the stabilisation of the mixed (HS:LS) state to low temperature for [MnIII(3-OMe-5-NO2-sal2323)]AsF6 and [MnIII(3-OMe-5-NO2-sal2323)]SbF6.

Shear viscoelasticity in anisotropic holographic axion model

Abstract In this work, we investigate the shear elasticity and the shear viscosity in a simple holographic axion model with broken translational symmetry and rotational symmetry in space via the perturbation computation. We find that, in the case of spontaneous symmetry breaking, the broken translations and anisotropy both enhance the shear elasticity of the system. While in all cases, the broken symmetries introduce a double suppression on the shear viscosity, which is in contrast to the result from the study of the p-wave holographic superfluid where the shear viscosity is enhanced when the rotational symmetry is broken spontaneously.

Bi-Josephson Effect in a Driven-Dissipative Supersolid

Abstract The Josephson effect is a macroscopic quantum tunneling phenomenon in a system with superfluid property, when it is split into two parts by a barrier. Here, we examine the Josephson effect in a driven-dissipative supersolid realized by coupling Bose-Einstein condensates to an optical ring cavity. We show that the spontaneous breaking of spatial translation symmetry in supersolid makes the location of the splitting barrier have a significant influence on the Josephson effect. Remarkably, for the same splitting barrier, depending on its location, two different types of DC Josephson currents are found in the supersolid phase (compared to only one type found in the superfluid phase). Thus, we term it a bi-Josephson effect. We examine the Josephson relationships and critical Josephson currents in detail, revealing that the emergence of supersolid order affects these two types of DC Josephson currents differently---one is enhanced, while the other is suppressed. The findings of this work unveil unique Josephson physics in the supersolid phase, and show new opportunities to build novel Josephson devices with supersolids.

Designing Chiral Organometallic Nanosheets with Room-Temperature Multiferroicity and Topological Nodes.

Two-dimensional (2D) room-temperature chiral multiferroic and magnetic topological materials are essential for constructing functional spintronic devices, yet their number is extremely limited. Here, by using the chiral and polar HPP (HPP = 4-(3-hydroxypyridin-4-yl)pyridin-3-ol) as an organic linker and transition metals (TM = Cr, Mo, W) as nodes, we predict a class of 2D TM(HPP)2 organometallic nanosheets that incorporate homochirality, room-temperature magnetism, ferroelectricity, and topological nodes. The homochirality is introduced by chiral HPP linkers, and the change in structural chirality induces a topological phase transition of Weyl phonons. The room-temperature magnetism arises from the strong d-p spin coupling between TM cations and HPP doublet anions. The ferroelectricity is attributed to the breaking of spatial inversion symmetry in the lattice structure. Additionally, by adjusting the type of TMs, these nanosheets show rich and tunable band structures. Notably, all predicted materials are topologically nontrivial, featuring a quadratic nodal point around the Fermi level.

S-d Coupling-Induced Dynamic Off-Centering of Cu Drives High Thermoelectric Performance in TlCuS.

Seeking new and efficient thermoelectric materials requires a detailed comprehension of chemical bonding and structure in solids at microscopic levels, which dictates their intriguing physical and chemical properties. Herein, we investigate the influence of local structural distortion on the thermoelectric properties of TlCuS, a layered metal sulfide featuring edge-shared Cu-S tetrahedra within Cu2S2 layers. While powder X-ray diffraction suggests average crystallographic symmetry with no distortion in CuS4 tetrahedra, the synchrotron X-ray pair distribution function experiment exposes concealed local symmetry breaking, with dynamic off-centering distortions of the CuS4 tetrahedra. The Cu off-centering is driven by the on-site coupling of filled 3d and unoccupied 4s orbitals (s-d) of Cu through a second-order Jahn-Teller mechanism. Bond softening by the p-d* (S-3p and Cu-3d) antibonding interaction coupled with dynamic off-centering distortions causes significant anharmonicity in the lattice, which acts as a phonon-blocking mechanism conducive to ultralow lattice thermal conductivity (κlat) (∼0.35-0.23 W m-1 K-1 in the ∼296-573 K temperature range) in TlCuS. The synergy between low κlat and multiband electronic structure leads to thermoelectric figure-of-merits (zT) of ∼1 and ∼1.3 at 573 K for pristine TlCuS and TlCu0.98S, respectively, underscoring the potential of metal sulfides as promising high-performance thermoelectrics.