Distinct Symmetry Research Articles

Dipolar Ising model: Phases, growth laws, and universality.

The behavior of many magnetic and dielectric solids, and the more contemporary magnetic superlattices, is governed by dipolar interactions. They are anisotropic and long ranged, having varied consequences ranging from ground states with complicated magnetic order to the presence of glassy dynamics characterized by a plethora of relaxation times. These systems are well captured by the dipolar Ising model (DIM) with nearest-neighbor exchange interactions (J) and long-range dipolar interactions (D). Depending on the relative interaction strength Γ=J/D, there are four phases of distinct magnetic order and symmetry. Using Monte Carlo simulations, we perform deep quenches to study domain growth or coarsening in the d=3 DIM. This important nonequilibrium phenomenon has not been addressed as dipolar interactions are notoriously difficult to handle theoretically. Our study reveals that, in spite of the anisotropy in interactions and diversity in ground state configurations, we observe universality in the ordering dynamics of all phases.

What are the crystallographic and genetic implications of a naturally occurring polycrystal composed of two mineral phases of distinct symmetries and anionic groups? The case study of 'joint occurrence' of emerald+alexandrite polycrystals from Brazil

What are the crystallographic and genetic implications of a naturally occurring polycrystal composed of two mineral phases of distinct symmetries and anionic groups? The case study of 'joint occurrence' of emerald+alexandrite polycrystals from Brazil

Crossover between distinct symmetries in solid solutions of rare earth nickelates

A strong coupling of the lattice to functional properties is observed in many transition metal oxide systems, such as the ABO3 perovskites. In the quest for tailor-made materials, it is essential to be able to control the structural properties of the compound(s) of interest. Here, thin film solid solutions that combine NdNiO3 and LaNiO3, two materials with the perovskite structure but distinct space groups, are analyzed. Raman spectroscopy and scanning transmission electron microscopy are combined in a synergistic approach to fully determine the mechanism of the structural crossover with chemical composition. It is found that the symmetry transition is achieved by phase coexistence in a way that depends on the substrate selected. These results carry implications for analog-tuning of physical properties in future functional materials based on these compounds.

Zirconolite from Larvik Plutonic Complex, Norway, its relationship to stefanweissite and nöggerathite, and contribution to the improvement of zirconolite end-member systematics

Abstract The very first description of zirconolite, originally called polymignyte, discovered in alkaline pegmatites within the Larvik Plutonic Complex (LPC), Norway, was published almost 200 yr ago. We studied zirconolite from three occurrences located in this region using modern techniques—X-ray powder diffraction (XRPD) upon thermal annealing of initially radiation-damaged mineral, electron probe microanalysis, and Mössbauer spectroscopy. The initial XRPD pattern lacked any sharp diffraction maxima, as the accumulated radiation dose exceeded a critical value of ca. 1016 α-decays/mg. Annealing at 400–800 °C induced recrystallization to a transitional, cubic phase interpreted to have a disordered, defect fluorite structure [space group Fm3m; unit-cell parameters: a = 5.1047(4) Å, V = 133.02(2) Å3], with its XRPD pattern being very similar to that of cubic ZrO2. Rietveld analysis of the XRPD pattern obtained after a phase transition at 900 °C shows a mixture of -3O [wt. fraction of ca. 60%, space group Cmca, unit-cell parameters: a = 7.2664(8) Å, b = 14.1877(15) Å, c = 10.1472(12) Å, V = 1046.1(2) Å3], and -3T [wt. fraction of ca. 40%, space group P3121, unit-cell parameters: a = 7.2766(6) Å, c = 17.0627(15) Å, V = 752.42(11) Å3] zirconolite polytypes. However, the crystal habits of zirconolite from the LPC show a distinct orthorhombic symmetry. Although their chemical compositions are far from the ideal zirconolite composition and a large number of elements are involved in high concentrations [up to ca. 17 wt% REE2O3, ≤7 wt% ACTO2, ≤18 wt% Me25+O5, ≤9 wt% Me2+O + Me23+O3, Fe3+/(Fe3++Fe2+) ≈ 0.2, where ACT = Th + U, Me5+ = Nb ± Ta, Me2+ = Fe2+ ± Mg, Me3+ ≈ Fe3+], the compositional variability is relatively limited. To quantitatively describe the two distinct compositional trends observed, we introduced a concept called “edgemembers,” so that mixing is approximated to occur between two terminal compositions situated at two edges of the zirconolite composition space. These marginal compositions were determined from observed compositional trends, i.e., heterovalent substitution of Me5+ for Ti in octahedral sites and ACT enrichment associated with increasing Ti/Me5+ ratio. This approach provides general substitution vectors for both, Håkestad-type mode (ACT + 3 Ti + Me3+ = Ca + 3 Me5+ + Me2+), and Stålaker-type mode (0.7 ACT + 0.5 REE + 0.9 Ti + 0.7 Me3+ + 0.05 Zr = 1.2 Ca + 1.3 Me5+ + 0.3 Me2+ + 0.05 Mn). In terms of chemical composition, the studied zirconolite corresponds to recently approved zirconolite-related minerals stefanweissite (for Ca > REE) and nöggerathite (for REE > Ca). Based on a careful analysis of zirconolite composition space, we show that our observed Håkestad-type compositional trend, as well as a high number of published zirconolite compositions worldwide (with Me2+ + Me3+ sum of ca. 1 atom per 14 O), can be well approximated by a modified end-member set comprising Ca2Zr2Me25+TiMe2+O14, REE2Zr2Ti3Me2+O14, CaACTZr2Ti3Me2+O14, CaREEZr2Ti3Me3+O14, and Ca2Zr2Ti2Me5+Me3+O14 without a need to involve the ideal zirconolite formula Ca2Zr2Ti4O14. The redefined composition space constrained by end-members from this set, together with ideal zirconolite, may be representative of the vast majority of more than 450 published zirconolite compositions worldwide with Me2+ + Me3+ totaling ≤1 atom per 14 O. The equation XMe3+ = 2 – 2XREE* – 3XMe5+* provides an independent calculation of iron oxidation state or XMe3+ = Me3+/(Me2+ + Me3+) for this remarkable group of zirconolites, where XREE* is derived from XREE = REE/(REE + Ca) and XMe5+* from XMe5+ = Me5+/(Me5+ + Ti). Understanding the oxidation state of iron in zirconolite may be helpful to characterize redox conditions during its crystallization.

Evaluation of Pearson correlation coefficient and Parisi parameter of replica symmetry breaking in a hybrid electronically addressable random fiber laser.

The hybrid electronically addressable random (HEAR) laser is a novel type of random fiber laser that presents the remarkable property of selection of the fiber section with lasing emission. Here we present a joint analysis of the correlations between intensity fluctuations at distinct wavelengths and replica symmetry breaking (RSB) behavior of the HEAR laser. We introduce a modified Pearson coefficient that simultaneously comprises both the Parisi overlap parameter and standard Pearson correlation coefficient. Our results highlight the contrast between the correlations and presence or not of RSB phenomenon in the spontaneous emission behavior well below threshold, replica-symmetric ASE regime slightly below threshold, and RSB phase with random lasing emission above threshold. In particular, in the latter we find that the onset of RSB behavior is accompanied by a stochastic dynamics of the lasing modes, leading to competition for gain intertwined with correlation and anti-correlation between modes in this complex photonic phase.

Third-order nonlinear Hall effect induced by the Berry-connection polarizability tensor.

Nonlinear responses in transport measurements are linked to material properties not accessible at linear order1 because they follow distinct symmetry requirements2-5. While the linear Hall effect indicates time-reversal symmetry breaking, the second-order nonlinear Hall effect typically requires broken inversion symmetry1. Recent experiments on ultrathin WTe2 demonstrated this connection between crystal structure and nonlinear response6,7. The observed second-order nonlinear Hall effect can probe the Berry curvature dipole, a band geometric property, in non-magnetic materials, just like the anomalous Hall effect probes the Berry curvature in magnetic materials8,9. Theory predicts that another intrinsic band geometric property, the Berry-connection polarizability tensor10, gives rise to higher-order signals, but it has not been probed experimentally. Here, we report a third-order nonlinear Hall effect in thick Td-MoTe2 samples. The third-order signal is found to be the dominant response over both the linear- and second-order ones. Angle-resolved measurements reveal that this feature results from crystal symmetry constraints. Temperature-dependent measurement shows that the third-order Hall response agrees with the Berry-connection polarizability contribution evaluated by first-principles calculations. The third-order nonlinear Hall effect provides a valuable probe for intriguing material properties that are not accessible at lower orders and may be employed for high-order-response electronic devices.

A study of curvature theory for different symmetry classes of Hamiltonian

We study and present the results of curvature for different symmetry classes (BDI, AIII and A) of model Hamiltonians and also present the transformation of model Hamiltonian from one distinct symmetry class to the other based on the curvature property. We observe the mirror symmetric curvature for the Hamiltonian with BDI symmetry class but there is no evidence of such behaviour for Hamiltonians of AIII symmetry class. We show the origin of torsion and its consequences on the parameter space of topological phase of the system. We find the evidence of torsion for the Hamiltonian of A symmetry class. We present Serret–Frenet equations for all model Hamiltonians in \(\mathbf {R}^3\) space. To the best of our knowledge, this is the first application of curvature theory to the model Hamiltonian of different symmetry classes which belong to the topological state of matter.

Multipolar topological field theories: Bridging higher order topological insulators and fractons

Two new recently proposed classes of topological phases, namely fractons and higher order topological insulators (HOTIs), share at least superficial similarities. The wide variety of proposals for these phases calls for a universal field theory description that captures their key characteristic physical phenomena. In this work, we construct topological multipolar response theories that capture the essential features of some classes of fractons and higher order topological insulators. Remarkably, we find that despite their distinct symmetry structure, some classes of fractons and HOTIs can be connected through their essentially identical topological response theories. More precisely, we propose a topological quadrupole response theory that describes both a 2D symmetry enriched fracton phase and a related bosonic quadrupolar HOTI with strong interactions. Such a topological quadrupole term encapsulates the protected corner charge modes and, for the HOTI, predicts an anomalous edge with fractional dipole moment. In 3D we propose a dipolar Chern-Simons theory with a quantized coefficient as a description of the response of both second order HOTIs harboring chiral hinge currents, and of a related fracton phase. This theory correctly predicts chiral currents on the hinges and anomalous dipole currents on the surfaces. We generalize these results to higher dimensions to reveal a family of multipolar Chern-Simons terms and related $\theta$-term actions that can be reached via dimensional reduction or extension from the Chern-Simons theories.

Switching Spinless and Spinful Topological Phases with Projective PT Symmetry.

A fundamental dichotomous classification for all physical systems is according to whether they are spinless or spinful. This is especially crucial for the study of symmetry-protected topological phases, as the two classes have distinct symmetry algebra. As a prominent example, the spacetime inversion symmetry PT satisfies (PT)^{2}=±1 for spinless/spinful systems, and each class features unique topological phases. Here, we reveal a possibility to switch the two fundamental classes via Z_{2} projective representations. For PT symmetry, this occurs when P inverses the gauge transformation needed to recover the original Z_{2} gauge connections under P. As a result, we can achieve topological phases originally unique for spinful systems in a spinless system, and vice versa. We explicitly demonstrate the claimed mechanism with several concrete models, such as Kramers degenerate bands and Kramers Majorana boundary modes in spinless systems, and real topological phases in spinful systems. Possible experimental realization of these models is discussed. Our work breaks a fundamental limitation on topological phases and opens an unprecedented possibility to realize intriguing topological phases in previously impossible systems.

Discrete and higher-form symmetries in SCFTs from wrapped M5-branes

We analyze topological mass terms of BF type arising in supersymmetric M-theory compactifications to AdS5. These describe spontaneously broken higher-form gauge symmetries in the bulk. Different choices of boundary conditions for the BF terms yield dual field theories with distinct global discrete symmetries. We discuss in detail these symmetries and their ’t Hooft anomalies for 4d mathcal{N} = 1 SCFTs arising from M5-branes wrapped on a Riemann surface without punctures, including theories from M5-branes at a ℤ2 orbifold singularity. The anomaly polynomial is computed via inflow and contains background fields for discrete global 0-, 1-, and 2-form symmetries and continuous 0-form symmetries, as well as axionic background fields. The latter are properly interpreted in the context of anomalies in the space of coupling constants.

Symmetries of abelian Chern-Simons theories and arithmetic

We determine the unitary and anti-unitary Lagrangian and quantum symmetries of arbitrary abelian Chern-Simons theories. The symmetries depend sensitively on the arithmetic properties (e.g. prime factorization) of the matrix of Chern-Simons levels, revealing interesting connections with number theory. We give a complete characterization of the symmetries of abelian topological field theories and along the way find many theories that are non-trivially time-reversal invariant by virtue of a quantum symmetry, including U(1)k Chern-Simons theory and (ℤk)ℓ gauge theories. For example, we prove that U(1)k Chern-Simons theory is time-reversal invariant if and only if −1 is a quadratic residue modulo k, which happens if and only if all the prime factors of k are Pythagorean (i.e., of the form 4n + 1), or Pythagorean with a single additional factor of 2. Many distinct non-abelian finite symmetry groups are found.

Bridging hexatic and tetratic phases in binary mixtures through near critical point fluctuations

Monte Carlo simulations were used to study the assembly of model binary mixtures whose pure components have either distinct or similar crystal order symmetry. Specifically, we simulated mixtures of hard disks with either squares or hexagons, where the components have size ratios that optimize their co-assembly into compositionally disordered solids. For the disks + squares mixture, along with the enhanced regions of solid miscibility, we report a continuous-looking transition from the disklike to the squarelike behavior that occurs through a region that seamlessly bridges the regions of hexatic phase of disks and the tetratic phase of squares, which we term the mosaic ($M$) region. For the equimolar composition, this $M$ region is bound by the isotropic phase at low pressures and by the hexatic-tetratic (two-phase) macrophase segregated region above a critical transition pressure. Our analysis showed that the $M$ region lies in the vicinity of the critical point, manifesting local compositional fluctuations that give rise to microphase segregated regions of interspersed square-rich fourfold and rhombic lattice symmetry and disk-rich sixfold clusters that coexist across the system. The $M$ behavior is characterized by a short-ranged translational order and an algebraic decay of the correlation functions for sixfold and fourfold orientational order. A finite size scaling analysis was used to evaluate the dependence of the local compositional susceptibility with system size to extract the critical exponent associated with the approach of the critical point. For the disks + hexagons mixture, a fully mixed hexatic phase was observed for all compositions.

Tunable Luminescence of Ce3+-Doped Calcium Boroaluminate Glasses for Light Emitting Devices

In this work, the visible luminescence of Ce3+-doped calcium boroaluminate glasses (CaBAl) was studied. Samples of CaBAl glass with composition (30.97-x)CaO-49.90B2O3-10.22Al2O3-8.90CaF2-xCeO2, with values of x varying from 0.25 to 1.25 mol.%, were prepared by the conventional melt-quenching technique, adding carbon as a reducing agent. The samples studied had amorphous nature confirmed by the results of X-ray diffraction (XRD). The Fourier transform infrared (FTIR) results showed that the vitreous network is formed by BO3 and BO4 structures, and the calculated values of the fraction of BO4 groups (N4) revealed that the increment of cerium favored the conversion of BO3 to BO4. The optical absorption spectra presented an intense broad band assigned to a charge transfer of the Ce4+, with a shift of ultraviolet (UV) absorption edge to longer wavelength, and a decrease in the band gap as result of the CeO2 concentration increase. The photoluminescence excitation (PLE) spectra showed that Ce3+-doped CaBAl glasses can be excited in a wide range of the UV spectral region (320-405 nm). The luminescence band of Ce3+ transitions 5d1 → 2F5/2, 2F7/2 was observed with different maximum in the emission bands for different excitation wavelengths, originate from Ce3+ ions placed mainly in two different sites in the glass network, resulting in distinct band positions and symmetries. The International Commission on Illumination (CIE) diagram demonstrated that the emission of samples occurs in the blue region. The lifetime decreased with increasing CeO2 concentration (47 to 34 ns) from 1.25 to 0.25 mol.% of CeO2. The results suggest that the studied glasses have potential for applications in optical devices such as LEDs and phosphors.

Nanostructure of a deep eutectic solvent at solid interfaces

HypothesisDeep eutectic solvents (DESs) are an attractive class of tunable solvents. However, their uptake for relevant applications has been limited due to a lack of detailed information on their structure-property relationships, both in the bulk and at interfaces. The lateral nanostructure of the DES-solid interfaces is likely to be more complex than previously reported and requires detailed, high-resolution investigation. ExperimentsWe employ a combination of high-resolution amplitude-modulated atomic force microscopy and molecular dynamics simulations to elucidate the lateral nanostructure of a DES at the solid-liquid interface. Specifically, the lateral and near-surface nanostructure of the DES choline chloride:glycerol is probed at the mica and highly-ordered pyrolytic graphite interfaces. FindingsThe lateral nanostructure of the DES-solid interface is heterogeneous and well-ordered in both systems. At the mica interface, the DES is strongly ordered via polar interactions. The adsorbed layer has a distinct rhomboidal symmetry with a repeat spacing of ~0.9 nm comprising all DES species. At the highly ordered pyrolytic graphite interface, the adsorbed layer appears distinctly different, forming an apolor-driven row-like structure with a repeat spacing of ~0.6 nm, which largely excludes the chloride ion. The interfacial nanostructure results from a delicate balance of substrate templating, liquid-liquid interactions, species surface affinity, and packing constraints of cations, anions, and molecular components within the DES. For both systems, distinct near-surface nanostructural layering is observed, which becomes more pronounced close to the substrate. The surface nanostructures elucidated here significantly expand our understanding of DES interfacial behavior and will enhance the optimization of DES systems for surface-based applications.

The Impact of Water on the Lateral Nanostructure of a Deep Eutectic Solvent–Solid Interface

Deep eutectic solvents (DESs) are tuneable solvents with attractive properties for numerous applications. Their structure–property relationships are still under investigation, especially at the solid–liquid interface. Moreover, the influence of water on interfacial nanostructure must be understood for process optimization. Here, we employ a combination of atomic force microscopy and molecular dynamics simulations to determine the lateral and surface-normal nanostructure of the DES choline chloride:glycerol at the mica interface with different concentrations of water. For the neat DES system, the lateral nanostructure is driven by polar interactions. The surface adsorbed layer forms a distinct rhomboidal symmetry, with a repeat spacing of ~0.9 nm, comprising all DES species. The adsorbed nanostructure remains largely unchanged in 75 mol-% DES compared with pure DES, but at 50 mol-%, the structure is broken and there is a compromise between the native DES and pure water structure. By 25 mol-% DES, the water species dominates the adsorbed liquid layer, leaving very few DES species aggregates at the interface. In contrast, the near-surface surface-normal nanostructure, over a depth of ~3 nm from the surface, remains relatively unchanged down to 25 mol-% DES where the liquid arrangement changed. These results demonstrate not only the significant influence that water has on liquid nanostructure, but also show that there is an asymmetric effect whereby water disrupts the nanostructure to a greater degree closer to the surface. This work provides insight into the complex interactions between DES and water and may enhance their optimization for surface-based applications.

Exceptional points in the one-dimensional Hubbard model

Non-Hermitian phenomena offer a novel approach to analyze and interpret spectra in the presence of interactions. Using the density-matrix renormalization group (DMRG), we demonstrate the existence of exceptional points for the one-particle Green’s function of the 1D alternating Hubbard chain with chiral symmetry, with a corresponding Fermi arc at zero frequency in the spectrum. They result from the non-Hermiticity of the effective Hamiltonian describing the Green’s function and only appear at finite temperature. They are robust and can be topologically characterized by the zeroth Chern number. This effect illustrates a case where temperature has a strong effect in 1D beyond the simple broadening of spectral features. Finally, we demonstrate that exceptional points appear even in the two-particle Green’s function (charge structure factor) where an effective Hamiltonian is difficult to establish, but move away from zero frequency due to a distinct symmetry constraint.

Distinct pairing symmetries of superconductivity in infinite-layer nickelates

We report theoretical predictions on the pairing symmetry of the newly discovered superconducting nickelate Nd$_{1-x}$Sr$_{x}$NiO$_{2}$ based on the renormalized mean-field theory for a generalized model Hamiltonian proposed in [Phys. Rev. B \textbf{101}, 020501(R)]. For practical values of the key parameters, we find a transition between a gapped ($d+is$)-wave pairing state in the small doping region to a gapless $d$-wave pairing state in the large doping region, accompanied by an abrupt Fermi surface change at the critical doping. Our overall phase diagram also shows the possibility of a ($d+is$)- to $s$-wave transition if the electron hybridization is relatively small. In either case, the low-doping ($d+is$)-wave state is a gapped superconducting state with broken time-reversal symmetry. Our results are in qualitative agreement with recent experimental observations and predict several key features to be examined in future measurements.

Orbital-enhanced warping effect in px,py-derived Rashba spin splitting of monatomic bismuth surface alloy

Spin-split Rashba bands have been exploited to efficiently control the spin degree of freedom of moving electrons, which possesses a great potential in frontier applications of designing spintronic devices and processing spin-based information. Given an intrinsic breaking of inversion symmetry and sizeable spin–orbit interaction, two-dimensional (2D) surface alloys formed by heavy metal elements exhibit a pronounced Rashba-type spin splitting of the surface states. Here, we have revealed the essential role of atomic orbital symmetry in the hexagonally warped Rashba spin-split surface state of the sqrt 3 times sqrt 3 R30^0 BiCu2 monatomic alloy by scanning tunneling spectroscopy (STS) and density functional theory (DFT). From dI/dU spectra and calculated band structures, three hole-like Rashba-split bands hybridized from distinct orbital symmetries have been identified in the unoccupied energy region. Because of the hexagonally deformed Fermi surface, quasi-particle interference (QPI) mappings have resolved scattering channels opened from interband transitions of px,py (mj = 1/2) band. In contrast to the s,pz-derived band, the hexagonal warping is predominately accompanied by substantial out-of-plane spin polarization Sz up to 24% in the dispersion of px,py (mj = 1/2) band with an in-plane orbital symmetry.

Influence of Aryl Substituents on the Alignment of Ligands in the Dirhodium Tetrakis(1,2,2‐Triarylcyclopropane‐ carboxylate) Catalysts

AbstractComputational studies revealed that dirhodium tetrakis(1,2,2‐triarylcyclopropanecarboxylate) (Rh2(TPCP)4) catalysts adopt distinctive high symmetry orientations, which are dependent on the nature of the aryl substitution pattern. The parent catalyst, Rh2(TPCP)4, and those with a p‐substituent at the C1 aryl, such as Rh2(p‐BrTPCP)4 and Rh2(p‐PhTPCP)4, adopt a C2‐symmetric structure. Rh2(3,5‐di(p‐tBuC6H4)TPCP)4, 3,5‐disubstituted at the C1 aryl, adopts a D2‐symmetric structure, whereas catalysts with an o‐substituent at the C1 aryl, such as Rh2(o‐Cl‐5‐BrTPCP)4, adopt a C4‐symmetric structure.

Novel results on entropy-based measures of fullerenes

Fullerenes are cubic polyhedral molecules made of carbon atoms. They have attracted much attention in the chemical and the mathematical literature. In the present paper, we compare the orbit and Hosoya entropies with the total energy of some classes of fullerenes to determine a correlation between these measures. Besides, we investigate the correlation between eigenvalues-based entropy and the total-energy of more than 400 fullerenes. Our findings reveal that the correlation between the adjacency energy, the eigenvalue-entropy, the total energy, the orbit-entropy, and the Hosoya-entropy of selected fullerenes with distinct symmetry groups is approximately equal to one.