Lattice Topology Research Articles

Development of novel superconductivity with higher Tc via the suppression of magnetism in quasi-two-dimensional electride Y2C under high pressures

Discovery of superconductivity in electride materials has been a topic of interest as their intrinsic electron-rich properties might suggest a considerable electron-phonon interaction. LayeredY2Cis a ferromagnetic quasi-two-dimensional electride with polarized anionic electrons confined in the interlayer space. In this theoretical study, we reportY2Cundergoes a series of structural phase transitions into two superconducting phases with estimatedTcof 9.2 and 21.0 K at 19 and 80 GPa, respectively, via the suppression of magnetism. Our extensive first-principles swarm structure searches identify that these two high-pressure superconducting phases possess an orthorhombicPnmaand a tetragonalI4/mstructures, respectively, where thePnmaphase is found to be a one-dimensional electride characterized by electron confinements in channel spaces of the crystal lattice, while the electride property inI4/mphase has been completely destroyed. We attribute the development of an unprecedentedly highTcsuperconductivity in Y-C system to the destructions of magnetism and the delocalization of interlayered anionic electrons under pressures. This work provides a unique example of pressure-induced collapse of magnetism at the onset of superconductivity in electride materials, along with the dramatic changes of electron-confinement topology in crystal lattices.

High-resolution three-dimensional imaging of topological textures in nanoscale single-diamond networks.

Topological defects-extended lattice deformations that are robust against local defects and annealing-have been exploited to engineer novel properties in both hard and soft materials. Yet, their formation kinetics and nanoscale three-dimensional structure are poorly understood, impeding their benefits for nanofabrication. We describe the fabrication of a pair of topological defects in the volume of a single-diamond network (space group Fd m) templated into gold from a triblock terpolymer crystal. Using X-ray nanotomography, we resolve the three-dimensional structure of nearly 70,000 individual single-diamond unit cells with a spatial resolution of 11.2 nm, allowing analysis of the long-range order of the network. The defects observed morphologically resemble the comet and trefoil patterns of equal and opposite half-integer topological charges observed in liquid crystals. Yet our analysis of strain in the network suggests typical hard matter behaviour. Our analysis approach does not require a priori knowledge of the expected positions of the nodes in three-dimensional nanostructured systems, allowing the identification of distorted morphologies and defects in large samples.

Realization of higher-order topological lattices on a quantum computer

Programmable quantum simulators may one day outperform classical computers at certain tasks. But at present, the range of viable applications with noisy intermediate-scale quantum (NISQ) devices remains limited by gate errors and the number of high-quality qubits. Here, we develop an approach that places digital NISQ hardware as a versatile platform for simulating multi-dimensional condensed matter systems. Our method encodes a high-dimensional lattice in terms of many-body interactions on a reduced-dimension model, thereby taking full advantage of the exponentially large Hilbert space of the host quantum system. With circuit optimization and error mitigation techniques, we measured on IBM superconducting quantum processors the topological state dynamics and protected mid-gap spectra of higher-order topological lattices, in up to four dimensions, with high accuracy. Our projected resource requirements scale favorably with system size and lattice dimensionality compared to classical computation, suggesting a possible route to useful quantum advantage in the longer term.

Ammonium Polyuranates: Old Dog, New Structural Tricks.

The crystal structure of ammonium polyuranates xUO3·yNH3·zH2O has been investigated. Powder X-ray diffraction (PXRD) has been employed to define single-phase samples within a series of synthesized compounds, which are further characterized by elemental analysis to ascertain the stoichiometry, revealing compositions of 3UO3·NH3·5H2O and 2UO3·NH3·3H2O. Analysis using extended X-ray absorption fine structure and vibrational spectroscopy has elucidated that both 3UO3·NH3·5H2O and 2UO3·NH3·3H2O possess a local structure similar to the metaschoepite─layered U(VI) oxohydroxide UO3·2H2O, but with H2O and NH4+ groups in the interlayers. The structures of ammonium polyuranates are solved from PXRD data, revealing their relationship to the U(VI) oxohydroxide with the established composition of NH4[(UO2)3O2(OH)3]·3H2O and NH4[(UO2)2O2(OH)]·2H2O for 3UO3·NH3·5H2O and 2UO3·NH3·H2O, respectively. These structures maintain the arrangement of U-O polyhedra as pentagonal bipyramids. However, disparities in lattice parameters, space group, and layer topology from UO3·2H2O emphasize significant structural modifications resulting from the substitution of water by ammonium. Moreover, the anion topology of the NH4[(UO2)2O2(OH)]·2H2O has no analogues among uranium oxohydroxide minerals. Notably, ammonium polyuranates, when compared, have minimal alterations in lattice parameters regardless of the presence of ammonia within the structure. The revealed results contribute valuable insights into the UO3-NH3-H2O system and hold potential applications in the field of nuclear power as ammonium polyuranates form during actinide precipitation in back-end of the nuclear fuel cycle and also serve as precursors in the fabrication of nuclear fuel.

Deformation mechanics of generalized missing rib chiral lattice structures

The planar missing rib lattice topology is generalized to construct a family of regular and irregular tetra-chiral periodic lattices. The geometry of a lattice in the family is completely defined by a set of six parameters. Using a unified energy based approach, the constitutive model and all effective elastic properties of the resulting lattice structures are determined from the unit periodic element of the lattice. Straightforward analytical expressions of the effective properties are obtained for some special geometries, which for the general case may be lengthy. In the latter case, the compliance tensor can easily be obtained numerically. The proposed approach involves accurate determination of the strain tensor and the compliance tensor for which a minimum error norm method is used. The results from the analytical expressions are compared with those obtained from Finite Element Analysis (FEA), and a very good match is observed. To draw a parity with experimental determination of the elastic properties and address the observation of auxeticity (negative Poisson’s ratio) in such lattice structures, the concept of empirical Young’s modulus and Poisson’s ratio is introduced. Using this idea, for the conventional chiral lattice, some disagreement in the existing literature is resolved.

Enhanced compressive mechanical properties of different topological lattice structures fabricated by additive manufacturing

This study focuses on the mechanical properties of 316 L stainless steel lattice structures. Three types of lattice structures with varying topology cells were designed and fabricated by additive manufacturing (AM) techniques. The experimental test and numerical simulation were employed to investigate compressive response and failure mechanisms of lattice structures. The results indicate that decreasing the porosity or unit cell size of lattice structures can significantly improve mechanical performance. Furthermore, it is noted that lattice structures with face-centered cubic with(vertical) Z-struts (FCCZ) cells exhibit the highest elastic modulus, compressive strength, and energy absorption, along with distinct failure modes in comparison to other types of lattice structures.

Modulation of Water Vapor Sorption by Pore Engineering in Isostructural Square Lattice Topology Coordination Networks.

We report a crystal-engineering study conducted upon a platform of three mixed-linker square lattice (sql) coordination networks of general formula [Zn(Ria)(bphy)] [bphy = 1,2-bis(pyridin-4-yl)hydrazine, H2Ria = 5-position-substituted isophthalic acid, and R = -Br, -NO2, and -OH; compounds 1-3]. Analysis of single-crystal X-ray diffraction data of 1-2 and the simulated crystal structure of 3 revealed that 1-3 are isomorphous and sustained by bilayers of sql networks linked by hydrogen bonds. Although similar pore shapes and sizes exist in 1-3, distinct isotherm shapes (linear and S shape) and uptakes (2.4, 11.6, and 13.3 wt %, respectively) were observed. Ab initio calculations indicated that the distinct water sorption properties can be attributed to the R groups, which offer a range of hydrophilicity. Calculations indicated that the significantly lower experimental uptake in compound 1 can be attributed to a constricted channel. The calculated water-binding sites provide insights into how adsorbed water molecules bond to the pore walls, with the strongest interactions, water-hydroxyl hydrogen bonding, observed for 3. Overall, this study reveals how pore engineering can result in large variations in water sorption properties in an isomorphous family of rigid porous coordination networks.

Exact counterdiabatic driving in finite topological lattice models

Adiabatic protocols are often employed in state preparation schemes but require the system to be driven by a slowly varying Hamiltonian so that transitions between instantaneous eigenstates are exponentially suppressed. Counterdiabatic driving is a technique to speed up adiabatic protocols by including additional terms calculated from the instantaneous eigenstates that counter diabatic excitations. However, this approach requires knowledge of the full eigenspectrum meaning that the exact analytical form of counterdiabatic driving is only known for a subset of problems, e.g., the harmonic oscillator and transverse field Ising model. We extend this subset of problems to include the general family of one-dimensional noninteracting lattice models with open boundary conditions and arbitrary onsite potential, tunneling terms, and lattice size. We will derive a general analytical form for the counterdiabatic term for all states of lattice models, including bound and in-gap states which appear, e.g., in topological insulators. We also derive the general analytical form of targeted counterdiabatic driving terms which are tailored to enforce the dynamical state to remain in a specific state. As an example of the use of the derived analytical forms, we consider state transfer using the topological edge states of the Su-Schrieffer-Heeger model. The derived analytical counterdiabatic driving Hamiltonian can be utilized to inform control protocols in many-body lattice models or to probe the nonequilibrium properties of lattice models. Published by the American Physical Society 2024

Experimental and numerical investigation of PLA based different lattice topologies and unit cell configurations for additive manufacturing

Experimental and numerical investigation of PLA based different lattice topologies and unit cell configurations for additive manufacturing

Delocalization and higher-order topology in a nonlinear elastic lattice

Topological elastic waves provide novel and robust ways for manipulating mechanical energy transfer and information transmission, with potential applications in vibration control, analog computation, and more. Recently discovered higher-order topological insulators (HOTIs) with multidimensional and hierarchical edge states can further expand the capabilities of topological elastic waves. However, the effects of nonlinearity on elastic HOTIs remain elusive. In this paper, we propose a nonlinear elastic higher-order topological Kagome lattice. After briefly reviewing its linear properties, we explore the effects of nonlinearity on the higher-order band topology and topological states. To do this, we have developed a method to calculate approximate nonlinear modes in order to identify the bulk polarization and probe the higher-order topological phase in the nonlinear lattice. We find that nonlinearity induces unusual delocalization of topological corner states, band crossing, and higher-order topological phase transition. The delocalization reveals that intracell hardening nonlinearity leads to direct delocalization of topological corner states while intracell softening nonlinearity first enhances and then reduces localization. The nonlinear higher-order topological phase is amplitude dependent, and we demonstrate a transition from a trivial to a non-trivial phase, enabling amplitude induced topological corner and edge states. Additionally, this phase transition corresponds to the closing and reopening of the bandgap, accompanied by an unusual band crossing. By examining the band topology before and after the band crossing, we find that the bulk polarization becomes quantized with respect to amplitude and can predict higher-order topological phases in nonlinear lattices. The obtained results are expected to be beneficial for the development of tunable and robust elastic wave devices.

Valley edge states with opposite chirality in temperature dependent acoustic media

The valley degree of freedom in phononic crystals and metamaterials holds immense promise for manipulating acoustic and elastic waves. However, the impact of acoustic medium properties on valley edge state frequencies and their robustness to one-way propagation in valley topological phononic crystals remains unexplored. While significant attention has been devoted to scatterer design embedded in honeycomb lattices within acoustic and elastic media to achieve valley edge states and topologically protected nontrivial bandgaps, the influence of variations in acoustic medium properties, such as wave velocity and density affected by environmental temperature, has been overlooked. In this study, we investigate the effect of valley edge states and topological phases exhibited by topological phononic lattices in a temperature-dependent acoustic medium. We observe that a decrease in wave velocity and density, influenced by changing environmental temperature, shifts the topological valley edge states to lower frequencies. Therefore, alongside phononic lattice design, it is crucial to consider the impact of acoustic medium properties on the practical application of acoustic topological insulators. This issue becomes particularly significant when a topological phononic crystal is placed in a wave medium that transitions from incompressible to compressible, where wave velocity and density are no longer constant. Our findings offer a novel perspective on investigating topological insulators in variable acoustic media affected by changing thermodynamic and fluid properties.

Numerical and Experimental Evaluation of Structured Material for Use in Multiscale Topology Optimization

Multiscale topology optimization is a powerful tool for engineers seeking a design with minimum weight and maximum stiffness, using a structured material in the form of a lattice structure. Furthermore, the current trend is to combine multiple lattice topologies in one component to achieve the best possible response to local loading conditions while minimizing weight. Therefore, herein, a numerical and experimental evaluation by compression tests in two directions is performed for six basic lattice topologies and two hypotheses are tested. The first hypothesis states that an additional weight saving of more than 30% can be achieved by a better choice of lattice topology. The second hypothesis is based on the manufacturing limitations of the laser powder bed fusion technology and the assumption that a favorable loading direction parallel to the building direction exists. The first hypothesis is only confirmed for loading in the direction parallel to the building direction and the second only for two lattice topologies. When both hypotheses are combined, the additional weight reduction of the multiscale topology optimization result is 44.5% according to the numerical results and 32.7% according to the experimental verification.

Unraveling the collinearity in short-range order parameters for lattice configurations arising from topological constraints.

In multicomponent lattice problems, for example, in alloys and at crystalline surfaces and interfaces, atomic arrangements exhibit spatial correlations that dictate the kinetic and thermodynamic phase behavior. These correlations emerge from interparticle interactions and are frequently reported in terms of the short-range order (SRO) parameter. Expressed usually in terms of pair distributions and other cluster probabilities, the SRO parameter gives the likelihood of finding atoms/molecules of a particular type in the vicinity of other atoms. This study focuses on fundamental constraints involving the SRO parameters that are imposed by the underlying lattice topology. Using a data-driven approach, we uncover the interrelationships between different SRO parameters (e.g., pairs, triplets, and quadruplets) on a lattice. The main finding is that while some SRO parameters are independent, the remaining are collinear, i.e., the latter are dictated by the independent ones through linear relationships. A kinetic and thermodynamic modeling framework based on these constraints is introduced.

On some Separation Axioms in Soft Lattice Topological Spaces

في عالم الطوبولوجيا، يتم فرض قيود مختلفة في كثير من الأحيان على أنواع الفضاءات الطوبولوجية قيد الدراسة ويتم تعريف هذه القيود من خلال ما يعرف ببديهيات الفصل. كما يمكن اعتبار بديهيات الفصل بمثابة شروط إضافية يمكن دمجها في تعريف الفضاءات الطوبولوجية. تخدم بديهيات الفصل أغراضًا مختلفة في نظرية الشبكة. أنها توفر أدوات لتصنيف ومقارنة الشبكات المختلفة، والكشف عن خصائصها الهيكلية والطوبولوجية. في حين أن بديهيات الفصل التقليدية مثل T0، T1، T2، وما إلى ذلك، لا تزال تلعب دورًا، فإن تفسيرها وآثارها تختلف في سياق المجموعات الناعمة والهياكل الشبكية. يقدم هذا البحث بديهيات الفصل، الفضاء T_i للشبكة الناعمة (لـ i = 4، 5، 6)، في سياق الفضاء الطوبولوجي للشبكة الناعمة ويبحث في العديد من الخصائص المرتبطة بها. يمكن لدراسة الشبكات من خلال هذه البديهيات أن تكشف عن الروابط بين خصائصها النظرية وخصائصها الطوبولوجية. يتجاوز هذا العمل مجرد تطبيق بديهيات الفصل على المساحات الطوبولوجية ذات الشبكة الناعمة. إنها تغامر بالكشف عن الخصائص الثابتة للشبكة الناعمة. بالإضافة إلى ذلك، تستكشف الدراسة الخصائص الثابتة للشبكة الناعمة المستمدة من مفاهيم T_i-space للشبكة الناعمة، وعلى وجه التحديد، الخصائص الطوبولوجية للشبكة الناعمة الوراثية والشبكة الناعمة. في الختام، فإن استكشاف الدراسة للخصائص الثابتة للشبكة الناعمة يدفع حدود فهم الفضاءات الطوبولوجية للشبكة الناعمة. ومن خلال الخوض في جوهر هذه الهياكل وخصائصها المحلية والعالمية، تفتح الدراسة الأبواب أمام إمكانيات نظرية مثيرة وتطبيقات محتملة في مجالات متنوعة.

Free-form acoustic topological waveguides enabled by topological lattice defects

Free-form acoustic topological waveguides enabled by topological lattice defects

Fracture of four semi-regular lattices regulated by T-stress in modified boundary layer models

The development of additive manufacturing technology has promoted the rise of various lattice metamaterials, and evaluating their fracture properties is critical for both application and safety. Here, by conducting finite element simulations on four types of elastic-brittle semi-regular lattices (kagome, snub-trihexagonal, elongated-triangular, and snub-square), we indicate that the fracture toughness of lattice metamaterials is not solely determined by the crack-tip singular term, i.e., the critical stress intensity factor, but is also influenced by the non-singular T-stress term. T-stress regulates fracture toughness by modulating geometrical distortions and force-carrying modes of lattice bars around the crack front. This regulation effect depends on the lattice topology and becomes weaker under mixed-mode loading. As the relative density of lattices decreases, T-stress can force elastic buckling of bars around the crack front, which may deteriorate the fracture toughness. Additionally, positive T-stress tends to promote the crack deflection and negative T-stress tends to inhibit. Our results offer new insights into the structure-property relationships in the presence of T-stress, which may contribute to design the geometry of micro/nano-lattice metamaterials.

Chirality-induced emergent spin-orbit coupling in topological atomic lattices

Chirality-induced emergent spin-orbit coupling in topological atomic lattices

Static vector solitons in a topological mechanical lattice

Topological solitons, renowned for their stability and particle-like collision behaviors, have sparked interest in developing macroscopic-scale information processing devices. However, the exploration of interactions between multiple topological solitons in mechanical systems remains elusive. In this study, we construct a topological mechanical lattice supporting static vector solitons that represent quantized degrees of freedom and can freely propagate across the system. Drawing inspiration from coupled double atomic chains with sublattice symmetry breaking, we design a mechanical analogue featuring topologically protected boundary modes and induce independent modes to finite motions along branched motion pathways. Through a continuum theory, we describe the evolution of boundary modes with vector solitons composed of superposed kink solutions, identifying them as minimum energy pathways on the rugged effective potential surface with multiple degenerate ground states. Our results reveal the connection between transformable topological lattices and multistable systems, providing insight into nonlinear topological mechanics.

A 3D printed ultra-short dental implant based on lattice structures and ZIRCONIA/Ca2SiO4 combination

Additive Manufacturing (AM) enables the generation of complex geometries and controlled internal cavities that are so interesting for the biomedical industry due to the benefits they provide in terms of osseointegration and bone growth. These technologies enable the manufacturing of the so-called lattice structures that are cells with different geometries and internal pores joint together for the formation of scaffold-type structures. In this context, the present paper analyses the feasibility of using diamond-type lattice structures and topology optimisation for the re-design of a dental implant. Concretely, a new ultra-short implant design is proposed in this work. For the manufacturing of the implant, digital light processing additive manufacturing technique technology is considered. The implant was made out of Nano-zirconia and Nano-Calcium Silicate as an alternative material to the more common Ti6Al4V. This material combination was selected due to the properties of the calcium-silicate that enhance bone ingrowth. The influence of different material combination ratios and lattice pore sizes were analysed by means of FEM simulation. For those simulations, a bio-material bone-nanozirconia model was considered that represents the final status after the bone is integrated in the implant. Results shows that the mechanical properties of the biocompatible composite employed were suitable for dental implant applications in dentistry. Based on the obtained results it was seen that those designs with 400 μm and 500 μm pore sizes showed best performance and led to the required factor of safety.

Hybrid ground-state quantum algorithms based on neural Schrödinger forging

Entanglement forging based variational algorithms leverage the bipartition of quantum systems for addressing ground-state problems. The primary limitation of these approaches lies in the exponential summation required over the numerous potential basis states, or bitstrings, when performing the Schmidt decomposition of the whole system. To overcome this challenge, we propose a method for entanglement forging employing generative neural networks to identify the most pertinent bitstrings, eliminating the need for the exponential sum. Through empirical demonstrations on systems of increasing complexity, we show that the proposed algorithm achieves comparable or superior performance compared to the existing standard implementation of entanglement forging. Moreover, by controlling the amount of required resources, this scheme can be applied to larger as well as non-permutation-invariant systems, where the latter constraint is associated with the Heisenberg forging procedure. We substantiate our findings through numerical simulations conducted on spin models exhibiting one-dimensional rings, two-dimensional triangular lattice topologies, and nuclear shell model configurations. Published by the American Physical Society 2024