Special Symmetry Research Articles

Bulk polarity of 3,5,7-trinitro-1-azaadamantane mediated by asymmetric NO2(lone pair)...NO2(π-hole) supramolecular bonding.

Molecular crystals exhibiting polar symmetry are important paradigms for developing new electrooptical materials. Though accessing bulk polarity still presents a significant challenge, in some cases it may be rationalized as being associated with the specific molecular shapes and symmetries and subtle features of supramolecular interactions. In the crystal structure of 3,5,7-trinitro-1-azaadamantane, C9H12N4O6, the polar symmetry of the molecular arrangement is a result of complementary prerequisites, namely the C3v symmetry of the molecules is suited to the generation of polar stacks and the inherent asymmetry of the principal supramolecular bonding, as is provided by NO2(lone pair)...NO2(π-hole) interactions. These bonds arrange the molecules into a trigonal network. In spite of the apparent simplicity, the structure comprises three unique molecules (Z'= 1/3+1/3+1/3), two of which are donors and acceptors of three N...O interactions and the third being primarily important for weak C-H...O hydrogen bonding. These distinct structural roles agree with the results of Hirshfeld surface analysis. A set of weak C-H...O and C-H...N hydrogen bonds yields three kinds of stacks. The orientation of the stacks is identical and therefore the polarity of each molecule contributes additively to the net dipole moment of the crystal. This suggests a special potential of asymmetric NO2(lone pair)...NO2(π-hole) interactions for the supramolecular synthesis of acentric materials.

Attentional Bias in specific symmetry and cleaning dimensions of obsessive-compulsive disorder

Attentional bias (AB) refers to increased allocation of attention on threat stimuli when compared to neutral stimuli. It is not clear if AB occurs in subjects with obsessive-compulsive disorder (OCD). We tested AB for symmetry and cleaning symptoms of OCD. Sixty-two patients with OCD and 40 healthy controls matched by gender, age and IQ, completed a computerized dot-probe task where two pictures (with symmetry or cleaning related content) were shown. The probe appeared in the location previously occupied by one of the pictures. Within-subjects linear mixed-effect models were used to investigate the effects of the factors: group (patients vs controls), OCD dimension (cleaning vs symmetry), task condition (neutral, congruent and incongruent), and the interaction among them. We also correlated AB scores with the clinical and demographic variables. No positive interaction resulted among the factors, but positive results were observed in group and condition, separately. Patients were significantly slower than controls (p-value = 0.014) (an effect that was accounted for by depression and anxiety symptoms and comorbidity) and the neutral condition was significantly faster when compared the other two conditions (congruent and incongruent, p-value = 0.013). No association was found between AB scores and clinical symptoms. There was no AB toward specific, content-related, stimuli in this sample of OCD patients.

Circuit implementation of a four-dimensional topological insulator

The classification of topological insulators predicts the existence of high-dimensional topological phases that cannot occur in real materials, as these are limited to three or fewer spatial dimensions. We use electric circuits to experimentally implement a four-dimensional (4D) topological lattice. The lattice dimensionality is established by circuit connections, and not by mapping to a lower-dimensional system. On the lattice’s three-dimensional surface, we observe topological surface states that are associated with a nonzero second Chern number but vanishing first Chern numbers. The 4D lattice belongs to symmetry class AI, which refers to time-reversal-invariant and spinless systems with no special spatial symmetry. Class AI is topologically trivial in one to three spatial dimensions, so 4D is the lowest possible dimension for achieving a topological insulator in this class. This work paves the way to the use of electric circuits for exploring high-dimensional topological models.

Topological phases in pseudospin-1 Fermi gases with two-dimensional spin-orbit coupling

The recent experimental realization of spin-orbit (SO) coupling for ultracold bosons and fermions opens an exciting avenue for engineering quantum matter that may be challenging to realize in solid state materials such as SO coupled spin-1 fermions. While one-dimensional SO coupling for spin-1 bosons has been experimentally realized, the generation of two-dimensional (2D) SO coupling and its topological properties are largely unexplored. Here we propose an experimental scheme for realizing a 2D Dresselhaus-type SO coupling in a square lattice for spin-1 Fermi gases. Because of the extended spin degree of freedom, many interesting topological phases could exist without relying on lattice point group symmetries that are crucial in solid state materials. These exotic phases include triply-degenerate points, quadratic band touching, a large Chern number ($C=5$) superfluid with 5 Majorana modes, triple-Weyl fermions, etc. Our scheme can be generalized to larger spins and provides a new route for engineering topological quantum matter by utilizing large spin degrees of freedom, instead of specific lattice symmetries.

Wishart planted ensemble: A tunably rugged pairwise Ising model with a first-order phase transition.

We propose the Wishart planted ensemble, a class of zero-field Ising models with tunable algorithmic hardness and specifiable (or planted) ground state. The problem class arises from a simple procedure for generating a family of random integer programming problems with specific statistical symmetry properties but turns out to have intimate connections to a sign-inverted variant of the Hopfield model. The Hamiltonian contains only 2-spin interactions, with the coupler matrix following a type of Wishart distribution. The class exhibits a classical first-order phase transition in temperature. For some parameter settings the model has a locally stable paramagnetic state, a feature which correlates strongly with difficulty in finding the ground state and suggests an extremely rugged energy landscape. We analytically probe the ensemble thermodynamic properties by deriving the Thouless-Anderson-Palmer equations and free energy and corroborate the results with a replica and annealed approximation analysis; extensive Monte Carlo simulations confirm our predictions of the first-order transition temperature. The class exhibits a wide variation in algorithmic hardness as a generation parameter is varied, with a pronounced easy-hard-easy profile and peak in solution time towering many orders of magnitude over that of the easy regimes. By deriving the ensemble-averaged energy distribution and taking into account finite-precision representation, we propose an analytical expression for the location of the hardness peak and show that at fixed precision, the number of constraints in the integer program must increase with system size to yield truly hard problems. The Wishart planted ensemble is interesting for its peculiar physical properties and provides a useful and analytically transparent set of problems for benchmarking optimization algorithms.

Skyrmion dynamics and topological sorting on periodic obstacle arrays

We examine skyrmions under a dc drive interacting with a square array of obstacles for varied obstacle size and damping. When the drive is applied in a fixed direction, we find that the skyrmions are initially guided in the drive direction but also move transverse to the drive due to the Magnus force. The skyrmion Hall angle, which indicates the difference between the skyrmion direction of motion and the drive direction, increases with drive in a series of quantized steps as a result of the locking of the skyrmion motion to specific symmetry directions of the obstacle array. On these steps, the skyrmions collide with an integer number of obstacles to create a periodic motion. The transitions between the different locking steps are associated with jumps or dips in the velocity–force curves. In some regimes, the skyrmion Hall angle is actually higher than the intrinsic skyrmion Hall angle that would appear in the absence of obstacles. In the limit of zero damping, the skyrmion Hall angle is 90°, and we find that it decreases as the damping increases. For multiple interacting skyrmion species in the collective regime, we find jammed behavior at low drives where the different skyrmion species are strongly coupled and move in the same direction. As the drive increases, the species decouple and each can lock to a different symmetry direction of the obstacle lattice, making it possible to perform topological sorting in analogy to the particle sorting methods used to fractionate different species of colloidal particles moving over two-dimensional obstacle arrays.

Magnetic forces in the absence of a classical magnetic field

It is shown that, in some cases, the effect of discrete distributions of flux lines in quantum mechanics can be associated with the effect of continuous distributions of magnetic fields with special symmetries. In particular, flux lines with an arbitrary value of magnetic flux can be used to create energetic barriers, which can be used to confine quantum systems in specially designed configurations. This generalizes a previous work where such energy barriers arose from flux lines with half-integer fluxons. Furthermore, it is shown how the Landau levels can be obtained from a two-dimensional grid of flux lines. These results suggest that the classical magnetic force can be seen as emerging entirely from the Aharonov-Bohm effect. Finally, the basic elements of a semi-classical theory that models the emergence of classical magnetic forces from fields with special symmetries are introduced.

Probe of topological invariants using quantum walks of a trapped ion in coherent state space**Project supported by the National Key R&D Program of China (Grant No. 2017YFA0304203), the National Natural National Science Foundation of China (Grant Nos. 11604392 and 11674200), the Changjiang Scholars and Innovative Research Team in Universities of Ministry of Education of China (Grant No. IRT 17R70), the

We present a protocol to realize topological discrete-time quantum walks, which comprise a sequence of spin-dependent flipping displacement operations and quantum coin tossing operations, with a single trapped ion. It is demonstrated that the information of bulk topological invariants can be extracted by measuring the average projective phonon number when the walk takes place in coherent state space. Interestingly, the specific chiral symmetry owned by our discrete-time quantum walks simplifies the measuring process. Furthermore, we prove the robustness of such bulk topological invariants by introducing dynamical disorder and decoherence. Our work provides a simple method to measure bulk topological features in discrete-time quantum walks, which can be experimentally realized in the system of single trapped ions.

Artificial intelligence for high-throughput discovery of topological insulators: The example of alloyed tetradymites

Significant advances have been made in predicting new topological materials using high-throughput empirical descriptors or symmetry-based indicators. To date, these approaches have been applied to materials in existing databases, and are severely limited to systems with well-defined symmetries, leaving a much larger materials space unexplored. Using tetradymites as a prototypical class of examples, we uncover a two-dimensional descriptor by applying an artificial intelligence (AI)-based approach for fast and reliable identification of the topological characters of a drastically expanded range of materials, without prior determination of their specific symmetries and detailed band structures. By leveraging this descriptor that contains only the atomic number and electronegativity of the constituent species, we have readily scanned a huge number of alloys in the tetradymite family. Strikingly, nearly half of them are identified to be topological insulators, revealing a much larger territory of the topological materials world. The present work also attests to the increasingly important role of such AI-based approaches in modern materials discovery.

The metaphysics of invariance

Fundamental physics contains an important link between properties of elementary particles and continuous symmetries of particle systems. For example, properties such as mass and spin are said to be 'associated' with specific continuous symmetries. This link has played a key role in the discovery of various new particle kinds, but more importantly: it is thought to provide a deep insight into the nature of physical reality.The link between properties and symmetries has been said to call for a radical revision of perceived metaphysical orthodoxy. However, if we are to use claims about a link between properties and symmetries in the articulation of metaphysical views, we first need to develop a sufficiently precise understanding of the content of these claims. The goal of this paper is to do just that.

Controlled growth of plasmonic heterostructures and their applications

Plasmonic nanocrystals with unique properties have been extensively studied in the past decades. A combination of plasmonic materials with other characteristic materials of metals and semiconductors leads to properties far beyond single-component materials and excellent performances in many optical-related applications. In this review, we summarize the recent advances in the controlled growth of plasmonic heterostructures with a specific composition, morphology, size, and structural symmetry. Plasmon-enhanced properties of the heterostructures and their excellent performances in applications are also discussed. The synthesis strategies and the intriguing properties of the plasmonic heterostructures provide great opportunity for applications in plasmon-enhanced nonlinear optics, optical spectroscopy, photocatalysis, solar energy conversion, and so on.

Amazing symmetrical clustering in chloroplast genomes

BackgroundPreviously, a seven-cluster pattern claiming to be a universal one in bacterial genomes has been reported. Keeping in mind the most popular theory of chloroplast origin, we checked whether a similar pattern is observed in chloroplast genomes.ResultsSurprisingly, eight cluster structure has been found, for chloroplasts. The pattern observed for chloroplasts differs rather significantly, from bacterial one, and from that latter observed for cyanobacteria. The structure is provided by clustering of the fragments of equal length isolated within a genome so that each fragment is converted in triplet frequency dictionary with non-overlapping triplets with no gaps in frame tiling. The points in 63-dimensional space were clustered due to elastic map technique. The eight cluster found in chloroplasts comprises the fragments of a genome bearing tRNA genes and exhibiting excessively high GC-content, in comparison to the entire genome.ConclusionChloroplasts exhibit very specific symmetry type in distribution of coding and non-coding fragments of a genome in the space of triplet frequencies: this is mirror symmetry. Cyanobacteria may have both mirror symmetry, and the rotational symmetry typical for other bacteria.

Spin‐Controlled Nonlinear Harmonic Generations from Plasmonic Metasurfaces Coupled to Intersubband Transitions

AbstractMetasurfaces that generate nonlinear optical responses provide new degrees of freedom for applications such as nonlinear holography, wave mixing, and new frequencies generation. To extend the utility of flat nonlinear optics, metasurfaces providing both giant nonlinear response for efficient frequency mixing in subwavelength films and a single‐beam output with a local wavefront control need to be developed. Metasurfaces with giant nonlinear response have recently been realized using the concept of intersubband polaritons. Separately, nonlinear metasurfaces providing a single‐beam nonlinear output with a local wavefront control have been studied. However, a metasurface platform that possesses both of these properties has yet to be demonstrated. Herein, the first such platform is presented and its operation for three‐ and four‐wave mixing processes is demonstrated. This approach is based on using Pancharatnam–Berry phase control of local nonlinear response and on employing meta‐atoms with specific symmetries to enable generation of only a single nonlinear beam. Experimentally, 400 nm‐thick metasurfaces with a wavefront‐controlled single‐beam output are demonstrated for second‐ and third‐harmonic generation at pump wavelength of approximately 10 µm. Power conversion efficiencies of 7.6 × 10−4% and 3.6 × 10−4% are obtained for the two nonlinear processes, respectively, at peak pumping intensity of only 80 kW cm−2.

The Dimensionality Transition between Three-Dimensional and Two-Dimensional Organic Microcrystals: Specific Symmetry and Selective Adhesion.

A three-dimensional–two-dimensional dimensionality transition of organic microcrystals was performed via elongated octahedrons, oblique octahedrons, diamond-like particles, and parallelograms using nonplanar 2,7-di(9H-carbazol-9-yl)spiro[fluorene-9,9′-xanthene] molecules. The specific crystal symmetry and selective adhesion of P123 on the {11–1}s facet are supposed to induce the morphological transition.

A hybrid symmetry–PSO approach to finding the self-equilibrium configurations of prestressable pin-jointed assemblies

For pin-jointed assemblies with many members or self-stress states, the form-finding problem using conventional methods generally involves considerable computational complexities due to the large size of the solution spaces. Here, we propose an improved form-finding method for prestressable pin-jointed structures by combining symmetry-based qualitative analysis with particle swarm optimization. Expressed in the symmetry-adapted coordinate system, the nodal coordinate vectors of a structure with specific symmetry and topology are independently extracted from the key blocks of the small-sized force density matrices associated with rigid-body translations. Then, the first block of the equilibrium matrix is computed, in which the null space reveals integral self-stress states. Particle swarm optimization is introduced and adapted to find feasible prestress modes, where the uniformity and unilaterality conditions of the members are considered. Besides, the QR decomposition with column pivoting is adopted for efficient computations on the null space of these blocks. The QR decompositions of the small-sized blocks of the force density matrix and the equilibrium matrix are performed iteratively, to simultaneously find a stable self-equilibrium configuration and a feasible prestress mode. Representative examples show the presented method is computationally efficient and accurate for the form-finding of symmetric tensegrities and prestressed cable–strut structures.

Aperiodic topological crystalline insulators

Topological crystalline insulators (TCIs) are usually described with topological protection imposed by the crystalline symmetry. In general, however, the existence of TCI states does not necessitate the periodicity of crystals as long as an essential lattice symmetry can be identified. Here we demonstrate the compatibility of TCIs with aperiodic systems, as exemplified by an octagonal quasicrystal. The aperiodic TCIs we proposed are attributed to a band inversion mechanism, which inverts states with the same parity but opposite eigenvalues of a specific symmetry (such as mirror reflection). The nontrivial topology is characterized by a nonzero integer ``mirror Bott index.'' Moreover, we demonstrate that the topological edge states and quantized conductance of the aperiodic TCI, which are robust against disorder, can be effectively manipulated by external electric fields. Our findings not only provide a better understanding of electronic topology in relation to symmetry but also extend the experimental realization of topological states to much broader material categories beyond crystals.

Improving fast-particle confinement in quasi-axisymmetric stellarator optimization

A method to improve fast-particle confinement during quasi-axisymmetric stellarator optimization has been identified. Quasi-axisymmetric (qa) stellarator designs have improved neoclassical transport due to their special symmetry of the magnetic field strength. Previously, it has been shown that, in general, quasi-symmetry can only be obtained on one single flux surface (Garren and Boozer 1991 Phys. Fluids B 3 2805–21). Even though quasi-symmetry can be a crucial property of stellarator design, there is no established convention for choosing the flux surface on which this should be optimized. To address this question, the flux surface on which quasi-axisymmetry is optimized has been varied in a qa configuration. The optimal location was found to lie between half radius and the plasma edge, since this allows for two beneficial features: it increases the number of flux-surfaces with improved quasi-axisymmetry and it increases the volume enclosed by the flux surface with the best qa quality.

Magnetic Interactions, Superconductivity, and Spin-Resonance Peak in Iron-Based Materials

Different mechanisms of superconductivity result in specific symmetries and structures of the gap in multiband systems. Here we review the spin fluctuation mechanism of Cooper pairing and discuss the spin resonance feature in the superconducting state of iron-based materials.

Electromagnetic Vorticity in a Square‐Well Crystal System Described by a Supersymmetric Wave‐Equation

AbstractVortices occur under all electromagnetic phenomena in quantized systems, as well as macroscopic systems. In particular, vorticity in square‐wells is of great appeal to the scientific community, as it models electromagnetic fields and formation of condensates in crystal lattices. A supersymmetric wave‐equation (SWE) is devised to model vorticity in a square‐well system, and the numerical results of several states of vorticity are shown by increased energy of the system. It is shown that square‐well vorticity obeys specific symmetries when modeled with the SWE and generates non‐overlapping vortices of the same spin. Nucleation of vortices when subjected to increased angular velocity and formation of giant vortices is also shown. This is of importance to the modeling of magnetism in quantum systems, and the generation of new results to describe quantum vorticity.

Resymmetrizing Broken Symmetry with Hydraulic Pressure.

Recent progress in condensed matter physics, such as for graphene, topological insulators, and Weyl semimetals, often originate from the specific topological symmetries of their lattice structures. Quantum states with different degrees of freedom, e.g., spin, valley, layer, etc., arise from these symmetries, and the coherent superposition of these states form multiple energy subbands. The pseudospin, a concept analogous to the Dirac spinor matrices, is a successful description of such multisubband systems. When the electron-electron interaction dominates, many-body quantum phases arise. They usually have discrete pseudospin polarizations and exhibit sharp phase transitions at certain universal critical pseudospin energy splittings. In this Letter, we present our discovery of hydrostatic-pressure-induced degeneracy between the two lowest Landau levels. This degeneracy is evidenced by the pseudospin polarization transitions of the fragile correlated quantum liquid phases near the Landau level filling factor ν=3/2. Benefitting from the constant hole concentration and the sensitive nature of these transitions, we study the fine-tuning effect of the hydrostatic pressure at the order of 10 μeV, well beyond the meV-level state-of-the-art resolution of other techniques.