High Symmetry Research Articles

Fabrication of Micro/Nano Dual Needle Structures with Morphological Gradient Based on Two-Photon Polymerization Laser Direct Writing with Proactive Focus Compensation

Micro/nano structures with morphological gradients possess unique physical properties and significant applications in various research domains. This study proposes a straightforward and precise method for fabricating micro/nano structures with morphological gradients utilizing single-voxel synchronous control and a nano-piezoelectric translation stage in a two-photon laser direct writing technique. To address the defocusing issue in large-scale fabrication, a methodology for laser focus dynamic proactive compensation was developed based on fluorescence image analysis, which can achieve high-precision compensation of laser focus within the entire range of the nano-piezoelectric translation stage. Subsequently, the fabrication of micro/nano dual needle structures with morphological gradients were implemented by employing different writing speeds and voxel positions. The minimum height of the tip in the dual needle structure is 80 nm, with a linewidth of 171 nm, and a dual needle total length reaching 200 μm. Based on SEM (scanning electron microscope) and AFM (atomic force microscope) characterization, the dual needle structures fabricated by the method proposed in this study exhibit high symmetry and nanoscale gradient accuracy. Additionally, the fabrication of hexagonal lattice periodic structures assembled from morphological gradient needle structures and the size gradient Archimedean spiral structures validate the capability of the single voxel-based fabrication and proactive focus compensation method for complex gradient structure fabrication.

A High Working Temperature Multiferroic Induced by Inverse Temperature Symmetry Breaking.

Molecular-based multiferroic materials that possess ferroelectric and ferroelastic orders simultaneously have attracted tremendous attention for their potential applications in multiple-state memory devices, molecular switches, and information storage systems. However, it is still a great challenge to effectively construct novel molecular-based multiferroic materials with multifunctionalities. Generally, the structure of these materials possess high symmetry at high temperatures, while processing an obvious order-disorder or displacement-type ferroelastic or ferroelectric phase transition triggered by symmetry breaking during the cooling processes. Therefore, these materials can only function below the Curie temperature (Tc), the low of which is a severe impediment to their practical application. Despite great efforts to elevate Tc, designing single-phase crystalline materials that exhibit multiferroic orders above room temperature remains a challenge. Here, an inverse temperature symmetry-breaking phenomenon was achieved in [FPM][Fe3(μ3-O)(μ-O2CH)8] (FPM stands for 3-(3-formylamino-propyl)-3,4,5,6-tetrahydropyrimidin-1-ium, which acts as the counterions and the rotor component in the network), enabling a ferroelastoelectric phase at a temperature higher than Tc (365 K). Upon heating from room temperature, two-step distinct symmetry breaking with the mm2Fm species leads to the coexistence of ferroelasticity and ferroelectricity in the temperature interval of 365-426 K. In the first step, the FPM cations undergo a conformational flip-induced inverse temperature symmetry breaking; in the second step, a typical ordered-disordered motion-induced symmetry breaking phase transition can be observed, and the abnormal inverse temperature symmetry breaking is unprecedented. Except for the multistep ferroelectric and ferroelastic switching, this complex also exhibits fascinating nonlinear optical switching properties. These discoveries not only signify an important step in designing novel molecular-based multiferroic materials with high working temperatures, but also inspire their multifunctional applications such as multistep switches.

Slow relaxation of magnetization in the Co(II)‐phosphotungstate Keggin polyoxometalate

AbstractWe are reporting the single crystal structure of the tetrabutylammonium (TBA) salt of the old Co(II) Keggin phosphotungstate anion (Co(II)POM) and a study of the magnetic behaviour of this well‐known POM. This Co(II)POM crystallizes in a cubic cell and this high symmetry obscure a precise characterization of Co(II) coordination sphere metrics due to positional disordered. We employed DFT and SA‐SOC‐CASSCF as auxiliary tools to complement DC and AC magnetic data collected. The studied complex behaves as a field‐induced single ion magnet (SIM) showing slow relaxing magnetization below 5 K under small DC applied magnetic fields. Raman relaxation mechanisms dominates with different relaxation times observed when switching from the TBA salt to the K salt of the Co(II)POM.

Ultra-wideband absorber based on graphene surface with polarization insensitivity under large angles

In this paper, a frequency-selective absorber with large-angular stability under oblique incidence is present. The absorptivity of the structure can be reached to maximum by impedance matching and parameter optimization method under a specific angle (40°), which ensures an excellent absorption response within 60° oblique incidence. This method solves the problem that the absorptivity of traditional absorbers deteriorates with the increase of incident angle. The absorber consists of a three-layer structure: two lossy layers and a metal ground layer, the equivalent circuit model is discussed and the operating frequency band is widened by generating electric resonances and magnetic resonances. Due to the high symmetry of the structure, the absorber has good polarization insensitivity. Numerical simulation shows that from 4.4 to 20 GHz, the absorptivity of the structure is above 90% within 40° oblique angle of incidence. Finally, the design plays an important role in military stealth and preventing electromagnetic interference.

Rapid Solid‐State Gas Sensing Realized via Fast K+ Transport Kinetics in Earth Abundant Rock‐Silicates

Here we report on the discovery of a novel fast potassium super stoichiometric silicate, with fully earth‐abundant nominal chemical composition of K2+xMg1−x/2SiO4, which exhibits near superionic K+ conductivity, up to 5 × 10−5 S cm−1 at room temperature. Fast K+ conduction is attributed to a high Continuous Symmetry Measure value in K‐polyhedrons, coupled with a low packing ratio of Corner‐Sharing‐framework. This is the first time that such a high conductivity is measured by a rock‐silicate formed only by abundant metal ions. K2+xMg1−x/2SiO4 displays excellent stability under air and humidity, which renders it a very promising candidate for economical fabrication of electrochemical devices such as potentiometric gas sensors. We demonstrated this by fabricating a gas sensor for SO2 detection, as the first demonstration of type III potentiometric gas sensors using K+ conductors. At 500 °C and SO2 concentrations in the range of 0–10 ppm, the sensor exhibited high sensitivities (69–72 mV dec−1), robust signal output (220 mV for 2 ppm of SO2), fast response times (1–6 min), and excellent stability in ambient condition.

Magnon bands in pyrochlore slabs with Heisenberg exchange and anisotropies

The pyrochlore lattice is a versatile venue to probe the properties of magnetically ordered states induced or perturbed by anisotropic terms like the Dzyaloshinskii–Moriya interactions or single-ion anisotropy. Several such ordered states have been investigated recently as precursors of topological magnons and the associated surface states. In parallel, there has been recent progress in growing thin films of magnetic materials with this lattice structure along high symmetry directions of the lattice. In both cases, an account of the magnetic excitations of relevant Hamiltonians for finite slabs is a necessary step in the analysis of the physics of these systems. While the analysis of bulk magnons for these systems is quite common, a direct evaluation of the magnon spectra in the slab geometry, though required, is less frequently encountered. We study here magnon bands in the slab geometry for a class of spin models on the pyrochlore lattice with Heisenberg exchange, Dzyaloshinskii–Moriya interaction and spin-ice anisotropy. For a range of model parameters, for both ferromagnetic and antiferromagnetic exchange, we compute the classical ground states for different slab orientations and determine the spin wave excitations above them. We analyze the ferromagnetic splay phase, the all-in-all-out (AIAO) phase and a coplanar phase and evaluate magnon dispersions for slabs oriented perpendicular to the [111], [100] and [110] directions. For all the phases considered, depending on the slab orientation, magnon band structures can be non-reciprocal and we highlight the differences in the three orientations from this point-of-view. Finally, we present details of the surface localized magnons for all the three slab orientations in the phases we study. For the ferromagnetic splay phase and the AIAO phase we analyze surface states associated with point degeneracies or nodal lines in the bulk spectrum by computing the magnonic Berry curvature and Weyl charges or Chern numbers associated with it.

High-Temperature Phase Transition with Switchable Dielectric Behavior and Significant Photoluminescence Changes in a Zero-Dimensional Hybrid SbBr6 Perovskite.

In the past decade, metal halide materials have been favored by many researchers because of their excellent physical and chemical properties under thermal, electrical, and light stimuli, such as ferroelectricity, dielectric, nonlinearity, fluorescence, and semiconductors, greatly promoting their application in optoelectronic devices. In this study, we successfully constructed an unleaded organic-inorganic hybrid perovskite crystal: [Cl-C6H4-(CH2)2NH3]3SbBr6 (1), which underwent a high-temperature reversible phase transition near Tp = 368 K. The phase transition behavior of 1 was characterized by differential scanning calorimetry, accompanied by a thermal hysteresis of 6 K. In addition, variable-temperature Raman spectroscopy analysis and PXRD further verified the sensitivity of 1 to temperature and the phase transition from low symmetry to high symmetry. Temperature-dependent dielectric testing shows that 1 can be a sensitive switching dielectric constant switching material. Remarkably, 1 exhibits strong photoluminescence emission with a wavelength of 478 nm and a narrow band gap of 2.7 eV in semiconductors. As the temperature increases and decreases, fluorescence undergoes significant changes, especially near Tc, which further confirms the reversible phase transition of 1. All of these findings provide new avenues for designing and assembling new phase change materials with high Tp and photoluminescence properties.

Abnormal Lower Limb Biomechanics During a Bilateral Vertical Jump Despite the Symmetry in Single-Leg Vertical Hop Height in Athletes After ACL Reconstruction.

A limb symmetry index (LSI) of >90% for single-leg horizontal hop distance is recommended as a cutoff point for safe return to sports after anterior cruciate ligament reconstruction (ACLR). Despite achieving this threshold, abnormal lower limb biomechanics continue to persist in athletes after ACLR. Symmetry in single-leg vertical hop height appears to be more difficult to achieve and can be a better representation of knee function than single-leg horizontal hop distance. To explore whether an LSI of >90% for single-leg vertical hop height can represent normal lower limb biomechanics in athletes during a bilateral vertical jump after ACLR. Controlled laboratory study. According to the LSI for single-leg vertical hop height, 46 athletes who had undergone ACLR with an autologous ipsilateral bone-patellar tendon-bone or hamstring tendon graft were divided into a low symmetry group (LSI <90%; n = 23) and a high symmetry group (LSI >90%; n = 23), and 24 noninjured athletes were selected as the control group. The kinematic and kinetic characteristics during a bilateral vertical jump were compared between the low symmetry, high symmetry, and control groups. During the propulsion phase of the bilateral vertical jump, the operated side in the high symmetry group showed a lower knee extension moment than the nonoperated side (P = .001). At peak vertical ground-reaction force, the operated side in the high symmetry group showed a lower knee internal rotation moment compared with the control group (P = .016). Compared with the nonoperated side, the operated side in the high symmetry group showed a higher hip extension moment (P = .002), lower knee extension moment (P < .001), lower ankle plantarflexion moment (P < .001), and lower vertical ground-reaction force (P = .023). Despite achieving an LSI of >90% for single-leg vertical hop height, athletes after ACLR showed abnormal lower limb biomechanical characteristics during the bilateral vertical jump. Symmetrical single-leg vertical hop height may not signify ideal biomechanical or return-to-sports readiness in this population.

Strain tuned structural, mechanical, electronic, and optical properties of lead-free oxy-nitride SrTaO2N perovskite using first-principles study

Recent advancements in perovskite-based solar energy conversion technologies require materials having enhanced optoelectronic properties and stability. Harnessing density functional theory (DFT), we have investigated here a novel orthorhombic phase of a recently synthesized oxynitride perovskite, SrTaO2N, and its uniaxial strain-tunable electronic and optical properties. Phonon dispersion and formation energy calculations are utilized to determine lattice dynamic stability and exothermic formation feasibility of the structure, correspondingly. The predicted bandgap at the Heyd–Scuseria–Ernzerhof [generalized gradient approximation Perdew–Burke–Ernzerhof (GGA-PBE)] level is ∼2.125 eV (∼1.125 eV), which is highly receptive to uniaxial strains. The bandgap formed in between X and G points with high symmetry at the first Brillouin zone was further dissected using the atomic orbital projected density of states (PDOS). The PDOS showed that the N-pz orbital dominantly contributes to valence band maxima and the Ta-dz2 orbital to conduction band minima. Compressive uniaxial strain widens the bandgap by ∼1.21 times, while tensile uniaxial strain lowers the bandgap by ∼1.1 times from the intrinsic value, suggesting strain switchable bandgap nature in the material. An elastic constant matrix also evaluates the mechanical stability of strained structures, and we found that in the strained structures from −6% to +6%, SrTaO2N is mechanically stable and ductile. Optical absorption reveals an increased absorption coefficient in the visible spectrum. These strain-tuned optoelectronic properties through the DFT approach thus suggest an evident route to a wide range of optoelectronics applications of the SrTaO2N perovskite material.

Internal-locking relativistic magnetron in transversely opposed driven scheme

A cascaded relativistic magnetron array with symmetric feeder structure was first proposed as a multi-port phase-coherent high-power microwave source, which is intrinsically equipped with high structural symmetry. Two symmetrically positioned slow-wave structures surround the feeder structure, which reduces axial electron drifting in each resonant system and ensures the phase-locking process. In this paper, a theory of structure-provided coupling coefficient and oscillator-required coupling coefficient is proposed as the phase-locking prerequisites. The method is evaluated by adopting two A6-type resonant systems. The symmetrically driven cascaded relativistic magnetron array employs a typical π-mode with an anode voltage of 450 kV and an axial magnetic field of 0.47 T. The phase-locked state was achieved in 17 ns with a jitter less than 5 deg. The total output power exceeds 2.3 GW at a frequency of 2.15 GHz, and the power flow in each output port exceeds 350 MW. The transversely opposed driven scheme can be combined with other phase-locking patterns for additional uses, and further optimization of resonant system could be applied for enhancing device performance. The theory of coupling prerequisites is also sufficient for analyzing other cascaded relativistic magnetrons.

Cluster energy prediction based on multiple strategy fusion whale optimization algorithm and light gradient boosting machine

BackgroundClusters, a novel hierarchical material structure that emerges from atoms or molecules, possess unique reactivity and catalytic properties, crucial in catalysis, biomedicine, and optoelectronics. Predicting cluster energy provides insights into electronic structure, magnetism, and stability. However, the structure of clusters and their potential energy surface is exceptionally intricate. Searching for the global optimal structure (the lowest energy) among these isomers poses a significant challenge. Currently, modelling cluster energy predictions with traditional machine learning methods has several issues, including reliance on manual expertise, slow computation, heavy computational resource demands, and less efficient parameter tuning.ResultsThis paper introduces a predictive model for the energy of a gold cluster comprising twenty atoms (referred to as Au20 cluster). The model integrates the Multiple Strategy Fusion Whale Optimization Algorithm (MSFWOA) with the Light Gradient Boosting Machine (LightGBM), resulting in the MSFWOA-LightGBM model. This model employs the Coulomb matrix representation and eigenvalue solution methods for feature extraction. Additionally, it incorporates the Tent chaotic mapping, cosine convergence factor, and inertia weight updating strategy to optimize the Whale Optimization Algorithm (WOA), leading to the development of MSFWOA. Subsequently, MSFWOA is employed to optimize the parameters of LightGBM for supporting the energy prediction of Au20 cluster.ConclusionsThe experimental results show that the most stable Au20 cluster structure is a regular tetrahedron with the lowest energy, displaying tight and uniform atom distribution, high geometric symmetry. Compared to other models, the MSFWOA-LightGBM model excels in accuracy and correlation, with MSE, RMSE, and R2 values of 0.897, 0.947, and 0.879, respectively. Additionally, the MSFWOA-LightGBM model possesses outstanding scalability, offering valuable insights for material design, energy storage, sensing technology, and biomedical imaging, with the potential to drive research and development in these areas.Graphical

Charge transfer boosts up methane adsorption and activation on three-coordinated metal sites

The activation and conversion of CH4 has attracted great interest due to its mitigation impact on the greenhouse gas and contribution to the high value-added chemicals. However, the activation of CH4 is the rate-limiting step due to the high symmetry of the molecule and its chemical inertness. In this study, we constructed active sites with specific geometry for methane activation based on the Nickel and other post-transition metals, where the interactions were significantly enhanced by 0.2∼0.6 eV varying with different VIII group metal types. With advanced electronic structure analysis methods, the origin of this interaction was unraveled, that is the Coulomb attraction induced by charge transfer from hydrogen of methane to three-coordinated metal Ni sites, rather than the covalent bonding or dispersion interaction. This enhancement not only increases the collision possibility by several orders of magnitude, but also lowers the barrier of CH bond breaking. These findings provide deep insight on the methane activation on metal catalysts and shed the light to design more efficient methane conversion catalysts.

Nodal phases in non-Hermitian wallpaper crystals

Symmetry and non-Hermiticity play pivotal roles in photonic lattices. While symmetries, such as parity-time (PT) symmetry, have attracted ample attention, more intricate crystalline symmetries have been neglected in comparison. Here, we investigate the impact of the 17 wallpaper space groups of two-dimensional crystals on non-Hermitian band structures. We show that the non-trivial space group representations enforce degeneracies at high symmetry points and dictate their dispersion away from these points. In combination with either T or PT, the symmorphic p4 mm symmetry and the non-symmorphic p2mg, p2gg, and p4gm symmetries protect exceptional chains intersecting at the pertinent high symmetry points.

Probabilistic rotation modeling based on directional mixture density networks

Predicting 3D rotations from a single image presents a significant challenge, primarily due to the inherent uncertainty arising from factors such as high symmetry, self-obscuration, and noise in the 3D environment. In this work, we propose a novel multimodal-based probabilistic model that integrates the matrix Fisher distribution and von Mises Fisher distribution into a mixture density network. Our model not only captures the inherent uncertainty of the object but also learns this uncertainty directly from the training data, thereby enhancing the robustness, flexibility, and efficiency of the model. To further refine the model's ability to handle ambiguities and recognize multiple distinct modes, we introduce a relaxed version of the winner-take-all loss function. This adaptation significantly improves the model's capability in accurately representing complex multimodal distributions. The performance of our model is rigorously assessed using two challenging datasets: Pascal3D+ and ModelNet10-SO(3). Extensive experimental analysis highlights the model's exceptional capability to fit complex multimodal distributions. Notably, when tested on the ModelNet10-SO(3) dataset, which is characterized by its ambiguity, and the more unequivocal Pascal3D+ dataset, our model outperforms the prevailing top baseline models by achieving accuracy improvements of 2.7% and 3.4%, respectively, at the minimum angle threshold. These results not only demonstrate our model's advanced capabilities in fitting complex distributions but also validate its effectiveness in accurately predicting 3D rotations in both ambiguous and unambiguous scenarios.

Diffusion Monte Carlo calculations of the polarizability of a confined hydrogen atom: benchmarking and application to high symmetry wells

We present a non-perturbative direct method to calculate the polarizability of a hydrogen atom confined in a three-dimensional potential well of any geometry. The calculation is based on the diffusion Monte Carlo method. The advantage of the method is simplicity of implementation and immediate adaptability to any well shape. The method is validated for the well-studied spherically confined hydrogen atom, and demonstrated in the case of two other geometries (cube and octahedron), for which this paper provides the first set of results. Although demonstrated here for the confined hydrogen atom, the method can be immediately applied to any single-electron system placed in a three-dimensional potential well of any type and geometry. Results for a hydrogen atom confined in potential wells of cubic or spherical symmetry suggests that the polarizability in these cases is a universal function of the volume of the well. This result can simplify calculations for real situations such as in quantum dots.

Extrinsic n-type semiconductor transition in ZrSe2 with the metallic character through hafnium substitution

Two-dimensional (2D) layered materials exhibit versatile electronic properties in their different phases. The intrinsic electronic properties of these materials can be modulated through doping or intercalation. In this study, we investigated the electronic properties of Hf-doped ZrSe2 single crystals using angle-resolved photoemission spectroscopy (ARPES) combined with first-principles density functional theory (DFT) calculations. It is observed that the valence band maxima of ZrSe2, located below the Fermi level, undergo a significant change with the introduction of Hf substitution. Hf can introduce extra charges into the conduction band, rather than making a mixed structure of HfSe2 and ZrSe2 band structure, which can cross the Fermi level. Compared to the semiconducting band structure of ZrSe2, we observed that the conduction band crosses the Fermi level at the high symmetry M point in Hf-doped ZrSe2. This suggests an increase of electron-type carriers around the Fermi level, resulting in an extrinsic charge carrier density in the conduction band, which can form a metallic behaviour. It can be noticed that the Hf cations can create disorder in the form of excess atoms of Zr, which yields more carriers in the conduction band in the shape of “smeared bands”. The tails of the “smeared band” occupied the d-orbitals extended into the Fermi level and left the d-band below. Similarly, the electrical resistance measurements further confirm the metallic-like character of Hf-doped ZrSe2 compared to the semiconductor ZrSe2, indicating increased carriers. This metallic-like behavior is suggested to be predisposed by the extrinsic electrons induced by the substitutional disorder. This study further demonstrates the possibility of band gap engineering through heavy metal doping in 2D materials.

How to Set the “Chirality” of Polyhedral Small Molecule Hydrocarbons: Decoration and Editing of Cubane Skeleton

AbstractSmall polyhedral hydrocarbons represented by cubane have attracted attention as potential molecular scaffolds for pharmaceuticals as benzene bioisoster. Cubane is also expected to be used as a chiral scaffold, but due to its high symmetry, it is necessary to introduce chirality by sequential site‐selective introduction of substituents. Furthermore, polyhedral desymmetrized isomers of cubane, such as cuneane and semibullvalene, and extended cage compounds, such as bishomocubane and homocuneane, exhibit chirality and are also expected to be used as new optically active scaffolds. In this concept, we would like to explain the synthetic routes we have planned, specifically, the decoration and editing of the cubane skeleton.

Single-Atom Alloys Materials for CO2 and CH4 Catalytic Conversion.

The catalytic conversion of greenhouse gases CH4 and CO2 constitutes an effective approach for alleviating the greenhouse effect and generating valuable chemical products. However, the intricate molecular characteristics characterized by high symmetry and bond energies, coupled with the complexity of associated reactions, pose challenges for conventional catalysts to attain high activity, product selectivity, and enduring stability. Single-atom alloys (SAAs) materials, distinguished by their tunable composition and unique electronic structures, confer versatile physicochemical properties and modulable functionalities. In recent years, SAAs materials demonstrate pronounced advantages and expansive prospects in catalytic conversion of CH4 and CO2. This review begins by introducing the challenges entailed in catalytic conversion of CH4 and CO2 and the advantages offered by SAAs. Subsequently, the intricacies of synthesis strategies employed for SAAs are presented and characterization techniques and methodologies are introduced. The subsequent section furnishes a meticulous and inclusive overview of research endeavors concerning SAAs in CO2 catalytic conversion, CH4 conversion, and synergy CH4 and CO2 conversion. The particular emphasis is directed toward scrutinizing the intricate mechanisms underlying the influence of SAAs on reaction activity and product selectivity. Finally, insights are presented on the development and future challenges of SAAs in CH4 and CO2 conversion reactions.

Modification of the Acoustic Mismatch Model and Diffuse Mismatch Model for Accurate Prediction of Interface Thermal Conductance At Low Temperatures

Abstract Houston&amp;amp;amp;amp;#39;s method for summing phonon modes in the Brillouin zone is applied to exclude specular transmission of phonon modes of specific symmetries, thus, modifying the Acoustic Mismatch Model when phonon heat flux is incident from a heavier to a lighter medium. The Houston method is also used to impose conservation of the number of phonons in each direction of high symmetry, thus modifying the detailed balance theorem and the Diffuse Mismatch Model. Based on the assumption that phonons are in equilibrium at the interface and are transmitted specularly or diffusely by two-phonon elastic processes, interpolation between the modified Acoustic Mismatch Model and the modified Diffuse Mismatch Model has led to a general analytical formalism for low-temperature interface thermal conductance. The Debye temperature, the only parameter in the derived formalism, is expressed as a function of temperature by assimilating numerically obtained specific heat values to the Debye expression for specific heat. Previous measurements of the thermal conductance of smooth and rough interfaces between dissimilar materials could be reproduced numerically without adjustment of model parameters, demonstrating the importance of modifications to the Acoustic Mismatch Model and the Diffuse Mismatch Model, and supporting the hypothesis that anharmonic processes play a minimal role in heat transport across interfaces below ambient temperature. The formalism developed is used to study the thermal conductance of the interface between silicon and germanium because of the potential of silicon-germanium nanocomposites for thermoelectric applications.

Heavy axions from twin dark sectors with [formula omitted]-characterized mirror symmetry

The QCD Lagrangian contains a CP violating gluon density term with a physical coefficient θ¯. The upper bound on the electric dipole moment of neutron requires the value of θ¯ to be extremely small. The tiny θ¯ is commonly known as the strong CP problem. In order to solve this puzzle, we construct a θ¯-characterized mirror symmetry between a pair of twin dark sectors with respective discrete symmetries. By taking a proper phase rotation of dark fields, we can perfectly remove the parameter θ¯ from the full Lagrangian. In our scenario, the discrete symmetry breaking, which are responsible for the mass generation of dark colored fermions and dark matter fermions, can be allowed near the TeV scale. This means different phenomena from the popular axion models with high scale Peccei-Quinn global symmetry breaking.