Nodal Surface Research Articles

Identification of conditions for ultrasonic effect on gas-dispersed medium and creation of radiators to increase the efficiency of coagulation in devices with swirling flow

Relevance. The presence and uncontrolled distribution of aerosols of various substances in the air, which have a negative impact on humans, flora and fauna. This problem is especially acute in the extraction, processing and combustion of georesources. The most effective way to solve the problem is the use of high-intensity ultrasonic vibrations, the effect of which on aerosols causes convergence and agglomeration of small particles into large ones. However, at low concentrations, the particle coagulation efficiency is not sufficient to increase the recovery rate of gas treatment equipment. Therefore, there is a need to find new ways to optimize ultrasonic equipment for coagulation of fine particles in order to increase its efficiency. Aim. To determine the optimal conditions for ultrasonic influence on a swirling gas-dispersed flow, ensuring maximum efficiency of agglomeration of highly dispersed particles. Carrying out comparative studies of coagulation of particles when exposed to ultrasonic fields generated by different types of radiators and their combined effects will make it possible to determine the effectiveness of ultrasonic coagulation and the optimal design scheme of ultrasonic exposure. Objects. Coagulation of particles under ultrasonic impact, formed by various types of radiators. Methods. Computer modeling of the generated ultrasonic field using the finite element method using harmonic acoustic analysis. Finite element modeling and design of disk radiators using modal analysis. To determine the characteristics of the aerosol, a Malvern Spraytec Particle Analyzer was used. Results. The results of calculations and experiments have shown that the use of an extended ultrasonic tubular radiator operating on a bending-diametric mode of vibration and forming a ring standing wave with a sound pressure level of 162–165 dB as the main source of ultrasonic impact for devices with swirling flows may be the most energy efficient. Further increase in the efficiency of coagulation can only be achieved by the combined action of a tubular radiator and a longitudinally oscillating radiator. This significantly modifies the field structure and provides not only an increase in the sound pressure level (up to 167 dB), but also in the number of formed nodal surfaces (up to 44).

Dimensionality-mediated type-II Dirac semimetal to quantum spin Hall insulator phase transition in TiC

We present first-principles results on monolayer (ML) and bulk titanium carbide (TiC) exhibiting dual topological characteristics: a quantum spin Hall insulator state in two-dimensional ML and a type-II Dirac semimetal state in its three-dimensional bulk form. The nontrivial nature of ML TiC is confirmed through the calculation of a Z2 invariant, spin Hall conductivity, and edge states. The edge band structure of ML TiC displays a single pair of gapless edge states at the M point. The insulating topological phase in ML TiC is driven by a band inversion around the M point involving Ti-d orbitals, with a nontrivial band gap of 0.47 eV. Our findings also indicate that ML TiC possesses excellent dynamical and thermal stability. Moreover, the bulk, ML hollow sphere arrays, and a 4-nm-thick film of TiC have already been synthesized, suggesting the high feasibility of the experimental synthesizing of ML TiC. On the other hand, we demonstrate that the bulk TiC hosts both a type-II Dirac cone and a topological nodal surface without spin-orbit coupling, protected by a combined symmetry of inversion and time reversal. The presence of spin-orbit coupling removes the nodal surface while preserving the type-II Dirac cone. Surface states connecting bulk Dirac nodes in bulk TiC can be readily observed, making the surface characteristics easily detectable in experiments. Published by the American Physical Society 2024

Flat-band and diverse quasi-fermions in Pb10(PO4)6O4

Employing a combination of first-principles calculations and low-energy effective models, we present a comprehensive investigation on the electronic structure of Pb10(PO4)6O4, which exhibits remarkable quasi-one-dimensional topological flat-band around the Fermi level. These flat bands predominantly originate from the px/py orbitals of the oxygen molecules chain at the fully-occupied 4e Wyckoff positions and thus can be well-captured by a minimal four-band tight-binding model. Furthermore, the abundant crystal symmetry inherent in Pb10(PO4)6O4 provides an ideal platform for the emergence of various quasi-fermions characterized by different dispersion, degeneracy, and dimensionality. These include a 0D four-fold degenerate Dirac fermion exhibiting quadratic dispersion, a 1D quadratic/linear nodal-line fermion along symmetric k-paths, a 1D hourglass nodal-line (HNL) fermion associated with the Dirac fermion, and a 2D symmetry-enforced nodal surface located on the kz = π plane. Moreover, when considering the weak ferromagnetic order, Pb10(PO4)6O4 transforms into a rare semi-half-metal, which is characterized by the presence of Dirac fermion and HNL fermion at the Fermi level for a single spin channel exhibiting 100 % spin polarization. Our findings reveal the rarely coexistence of flat bands, diverse topological semimetal states and ferromagnetism in Pb10(PO4)6O4, which may provide valuable insights for further exploring the intriguing interplay between superconductivity and exotic electronic states.

Verification of Adjoint Solution Commutativity with the New OpenNode Nodal Diffusion Code

This paper presents in-depth exploration and verification of the OpenNode nodal diffusion code, a robust tool designed for multigroup neutron diffusion simulations under steady-state conditions. Leveraging the Nodal Expansion Method with a quartic polynomial and moments weighting method, OpenNode demonstrates exceptional accuracy in approximating nodal surface fluxes, further enhanced by the Quadratic Transverse Leakage approximation. The critical concept of commutativity between adjoint and forward solutions is thoroughly investigated, serving as a benchmark for the code’s reliability in predicting system responses, determining single-point reactor kinetics parameters, and facilitating perturbation analyses. The paper meticulously details OpenNode’s methodology for adjoint neutron flux computation, unraveling its rigorous approach through transposition operations and intricate mathematical transformations. Noteworthy features, including support for second and fourth polynomial orders; versatile computation modes; different mesh points; and seamless integration with Python, PyQt5, and Blender, underscore OpenNode’s adaptability. Results from comprehensive analysis of the two-dimensional and three-dimensional International Atomic Energy Agency core benchmark problem showcase OpenNode’s prowess. The code excels in reactor geometry visualizations, benchmark parameters, and neutronic analysis, with a particular emphasis on commutativity verification against various benchmarked codes. The precision of OpenNode is further demonstrated in power distribution analyses, revealing remarkable proximity to reference values and symmetrical power distribution patterns.

Beyond Single-Reference Fixed-Node Approximation in Ab Initio Diffusion Monte Carlo Using Antisymmetrized Geminal Power Applied to Systems with Hundreds of Electrons.

Diffusion Monte Carlo (DMC) is an exact technique to project out the ground state (GS) of a Hamiltonian. Since the GS is always bosonic, in Fermionic systems, the projection needs to be carried out while imposing antisymmetric constraints, which is a nondeterministic polynomial hard problem. In practice, therefore, the application of DMC on electronic structure problems is made by employing the fixed-node (FN) approximation, consisting of performing DMC with the constraint of having a fixed, predefined nodal surface. How do we get the nodal surface? The typical approach, applied in systems having up to hundreds or even thousands of electrons, is to obtain the nodal surface from a preliminary mean-field approach (typically, a density functional theory calculation) used to obtain a single Slater determinant. This is known as single reference. In this paper, we propose a new approach, applicable to systems as large as the C60 fullerene, which improves the nodes by going beyond the single reference. In practice, we employ an implicitly multireference ansatz (antisymmetrized geminal power wave function constraint with molecular orbitals), initialized on the preliminary mean-field approach, which is relaxed by optimizing a few parameters of the wave function determining the nodal surface by minimizing the FN-DMC energy. We highlight the improvements of the proposed approach over the standard single-reference method on several examples and, where feasible, the computational gain over the standard multireference ansatz, which makes the methods applicable to large systems. We also show that physical properties relying on relative energies, such as binding energies, are affordable and reliable within the proposed scheme.

Discovery of Higher-Order Nodal Surface Semimetals.

The emergent higher-order topological insulators significantly deepen our understanding of topological physics. Recently, the study has been extended to topological semimetals featuring gapless bulk band nodes. To date, higher-order nodal point and line semimetals have been successfully realized in different physical platforms. However, for the conceptually expected higher-order nodal surface semimetals, a concrete model has yet to be proposed, let alone experimentally observed. Here, we report an ingenious design route for constructing this unprecedented higher-order topological phase. The three-dimensional model, layer-stacked with a two-dimensional anisotropic Su-Schrieffer-Heeger lattice, exhibits appealing hinge arcs connecting the projected nodal surfaces. Experimentally, we realize this new topological phase in an acoustic metamaterial, and present unambiguous evidence for both the bulk nodal structure and hinge arc states, the two key manifestations of the higher-order nodal surface semimetal. Our findings can be extended to other classical systems such as photonic, elastic, and electric circuit systems, and open new possibilities for controlling waves.

Inverse Designing Surface Curvatures by Deep Learning

Smooth and curved microstructural topologies found in nature—from soap films to trabecular bone—have inspired several mimetic design spaces for architected metamaterials and bio‐scaffolds. However, the design approaches so far are ad hoc, raising the challenge: how to systematically and efficiently inverse design such artificial microstructures with targeted topological features? Herein, surface curvature is explored as a design modality and a deep learning framework is presented to produce topologies with as‐desired curvature profiles. The inverse design framework can generalize to diverse topological features such as tubular, membranous, and particulate features. Moreover, successful generalization beyond both the design and data space is demonstrated by inverse designing topologies that mimic the curvature profile of trabecular bone, spinodoid topologies, and periodic nodal surfaces for application in bio‐scaffolds and implants. Lastly, curvature and mechanics are bridged by showing how topological curvature can be designed to promote mechanically beneficial stretching‐dominated deformation over bending‐dominated deformation.

Enhanced optical vector bottle beams with obscured nodal surfaces

Optical bottle beams, characterized by their unique three-dimensional dark core, have garnered substantial interest due to their potential applications across multiple domains of science and technology. This paper delves into the current methods used to create these beams and provides a method to obscure their nodal planes through coaxial non-interfering orthogonally polarized beams to generate bottle beams with enhanced uniformity. Experimental and theoretical results show the enhanced vector bottle beam maintains a smaller, more spherically uniform potential well and interesting quasi-particle polarization characteristics.

Nodal quintic surfaces and lines on cubic fourfolds (with an appendix by John Christian Ottem)

We study nodal quintic surfaces with an even set of 16 nodes as analogues of singular Kummer surfaces. The interpretation of the natural double cover of an even 16 -nodal quintic as a certain Fano variety of lines could be viewed as a replacement for the additive structure of the cover of a singular Kummer surface by its associated abelian surface. Most of the results in this article can be seen as refinements of known facts and our arguments rely heavily on techniques developed by Beauville (1979), Murre (1972), and Voisin (1986), Results due to Shen (2012, 2014) are particularly close to some of the statements. In this sense, the text is mostly expository (but with complete proofs), although our arguments often differ substantially from the original sources.

PT -symmetric non-Hermitian Hopf metal

The Hopf insulator is a representative class of three-dimensional topological insulators beyond the standard topological classification methods based on K theory. In this Letter, we describe the metallic counterpart of the Hopf insulator in non-Hermitian systems. While the Hopf invariant is not a stable topological index due to the additional non-Hermitian degree of freedom, we show that the PT symmetry stabilizes the Hopf invariant even in the presence of the non-Hermiticity. In sharp contrast to the Hopf insulator phase in the Hermitian counterpart, we describe an interesting result that the non-Hermitian Hopf bundle exhibits topologically protected non-Hermitian degeneracy, characterized by the two-dimensional surface of exceptional points. Despite the non-Hermiticity, the Hopf metal has the quantized Zak phase, which results in bulk-boundary correspondence by showing drumheadlike surface states at the boundary. Finally, we show that, by breaking PT symmetry, the nodal surface deforms into knotted exceptional lines. Our description of the Hopf metal phase confirms the existence of the non-Hermitian topological phase outside the framework of the standard topological classifications. Published by the American Physical Society 2024

Coexistence of electron and phonon topology in conjunction with quantum transport device modeling

The escalating research in the field of topology necessitates an understanding of the underlying rich physics behind the materials possessing unique features of non-trivial topology in both electronic and phononic states. Due to the interaction between electronic quasiparticles and spin degrees of freedom, the realization of magnetic topological materials has opened up a new frontier with unusual topological phases, however, these are rarely reported alongside phononic quasiparticle excitations. In this work, by first-principles calculations and symmetry analysis, the intermetallic ferromagnetic compounds MnGaGe and MnZnSb with the coexistence of exceptional topological features in the electronic and phononic states are proposed. These compounds host nodal surface on ky=π plane in bulk Brillouin zone in the electronic and phononic spectra protected by the combination of time-reversal symmetry and nonsymmorphic two-fold screw-rotation symmetry. In the former case, a spin-polarized nodal surface is present in the majority and minority spin channels and found to be robust to ground-state magnetic polarization. The presence of nodal line features is analyzed in both the quasiparticle spectra, whose non-trivial nature is confirmed by the Berry phase calculation. The incorporation of spin–orbit coupling in the electron spectra introduces distinctive characteristics in the transport properties, facilitating the emergence of anomalous Hall conductivity through Berry curvature in both bulk and monolayer. Furthermore, the monolayer has been proposed as a two-terminal device model to investigate the quantum transport properties using the non-equilibrium Green’s function approach. This superlative combination of observations and modeling sets the path for a greater level of insight into the behavior and aspects of topological materials at the atomic scale.

Coexistence of topological node surface and Dirac fermions in phonon-mediated superconductor YB2C2.

The interaction between nontrivial topology and superconductivity in condensed matter physics has attracted tremendous research interest as it could give rise to exotic phenomena. Herein, based on first-principles calculations, we investigate the electronic structures, mechanical properties, topological properties, dynamic stability, electron-phonon coupling (EPC), and superconducting properties of the synthesized real material YB2C2. It is a tetragonal structure with P4/mbm symmetry and exhibits excellent stability. The calculated electronic band structures reveal that a zero-dimension (0D) Dirac point and two-dimensional (2D) nodal surface coexist near the Fermi level. A spin-orbit coupling (SOC) Dirac point with the topological Fermi arc is observed on the (001) surface. These nodal surfaces are protected by a two-fold screw axis and time-reversal symmetry. Based on the Bardeen-Cooper-Schrieffer theory, the superconducting transition temperature (Tc) in the range 1.25-4.45 K with different Coulomb repulsion constant μ* for YB2C2 is estimated to be consistent with previous experimental results. In addition, the EPC is mainly from the coupling between the dx2-y2 and dz2 orbitals of the Y atom and low-energy phonon modes. The presence of superconductivity and nontrivial topological surface state in YB2C2 suggests that it may be a candidate material for topological superconductors.

Variations of topological surface states of nodal line semimetal AlB<sub>2</sub> after adsorption in aqueous environment

Topological semimetals have aroused great research interest due to their intrinsic topological physics and potential applications in devices. A key feature for all topological materials is the so-called bulk-boundary correspondence, which means that if there is non-trivial band topology in the bulk, then we can expect unique topologically protected conducting states in the surface, i.e. the topological surface state (TSS). Previously, the studies of the surface states of topological materials mainly focused on the pristine surfaces, while the topological nodal line semimetal surface states with adsorbates are rarely systematically studied. In this paper, the topological properties of the topological semimetal AlB<sub>2</sub> are studied by first-principles calculations, and the TSS position is calculated by constructing the Al- and B-terminated slab models. Observing the topological surface state, it is found that the drumhead-like TSS connects two Dirac nodes with no energy gaps on the node line, and the TSS of the Al end-terminated slab has a smaller energy dispersion than that of the B-terminated slab. The adsorption characteristics of AlB<sub>2</sub> (010) surface are studied, and it is found that the Gibbs free energy (<inline-formula><tex-math id="M2">\begin{document}$ {\Delta }{G}_{{{\mathrm{H}}}^{*}} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20240404_M2.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20240404_M2.png"/></alternatives></inline-formula>) for hydrogen adsorption on the surface of Al is only –0.031 eV, demonstrating excellent hydrogen evolution reaction (HER) performance. The changes of TSS after H, OH and H<sub>2</sub>O are adsorbed on the surface of AlB<sub>2</sub> in aqueous solution environment are observed. The TSS change is the most significant when H is adsorbed, followed by OH adsorption. And the influence of H<sub>2</sub>O on TSS due to its electrical neutrality and weak surface adsorption is very weak. Before and after adsorption, because the topology protection TSS still exists, only the energy changes, which confirms its robustness in the environment. The results of this work provide a systematic understanding of the effects of different adsorbents on the TSS of AlB<sub>2</sub>, paving the way for future theoretical and experimental research in related fields, and alsopresent theoretical support for putting the topological materials into practical applications .

TurboGenius: Python suite for high-throughput calculations of ab initio quantum Monte Carlo methods

TurboGenius is an open-source Python package designed to fully control ab initio quantum Monte Carlo (QMC) jobs using a Python script, which allows one to perform high-throughput calculations combined with TurboRVB [Nakano et al. J. Phys. Chem. 152, 204121 (2020)]. This paper provides an overview of the TurboGenius package and showcases several results obtained in a high-throughput mode. For the purpose of performing high-throughput calculations with TurboGenius, we implemented another open-source Python package, TurboWorkflows, that enables one to construct simple workflows using TurboGenius. We demonstrate its effectiveness by performing (1) validations of density functional theory (DFT) and QMC drivers as implemented in the TurboRVB package and (2) benchmarks of Diffusion Monte Carlo (DMC) calculations for several datasets. For (1), we checked inter-package consistencies between TurboRVB and other established quantum chemistry packages. By doing so, we confirmed that DFT energies obtained by PySCF are consistent with those obtained by TurboRVB within the local density approximation (LDA) and that Hartree–Fock (HF) energies obtained by PySCF and Quantum Package are consistent with variational Monte Carlo energies obtained by TurboRVB with the HF wavefunctions. These validation tests constitute a further reliability check of the TurboRVB package. For (2), we benchmarked the atomization energies of the Gaussian-2 set, the binding energies of the S22, A24, and SCAI sets, and the equilibrium lattice parameters of 12 cubic crystals using DMC calculations. We found that, for all compounds analyzed here, the DMC calculations with the LDA nodal surface give satisfactory results, i.e., consistent either with high-level computational or with experimental reference values.

A topological nodal surface carbon honeycomb for sodium-ion battery anode

Motivated by the successful synthesis of three-dimensional (3D) graphene monoliths, we propose a 3D carbon honeycomb structure, tC40, composed of graphene-nanoribbons linked with 5-5-8 defects based on first-principles calculations. This structure is not only dynamically, thermally, and mechanically stable, but also possesses interesting electronic properties, including the multiple topological nodal surfaces on the high-symmetry plane k3=0 with double and quadruple degeneracies of bands in the reciprocal space, and the nontrivial surface states connecting different topological nodal surfaces parallel to the z-axis. By using the k·p model, we further show that, unlike previously reported nodal surfaces, the energy dispersion of the quadruply degenerated nodal surface is proportional to the k32, while the Hamiltonian of the doubly degenerated nodal surface is formed by the essential degeneracy of the valence and conduction bands. In addition, we explore the application of this nodal surface carbon as an anode material for sodium-ion batteries (SIBs), and find that tC40 exhibits good performance with a high reversible capacity of 186 mAh·g−1, a low sodium ion migration barrier of 0.1 eV, and a small charging/discharging volume change of 0.79 %. This work expands the family of topological carbon materials and their applications in SIBs.

Monolayer TiC—A high-performance Dirac anode with ultralow diffusion barriers and high energy densities for Li-ion and Na-ion batteries

Two-dimensional Dirac materials have stimulated substantial research interest as binder-free anodes in metal-ion batteries, owing to their ultrahigh electronic conductivity, large specific area, and higher energy density. Here, using first-principles density functional theory calculations, we have investigated the feasibility of monolayer TiC as a potential anode material for Li/Na-ion batteries. The results indicate that monolayer TiC exhibits excellent dynamical and thermal stability. The electronic structure of monolayer TiC shows semimetallic characteristics with a Dirac cone at the M high symmetry point and the formation of Ti or C vacancies transforms the Dirac cone into a nodal loop or a nodal surface, respectively. Thus, monolayer TiC possesses superior electrical conductivity, which can be further enhanced by the formation of Ti or C vacancies in the material. Furthermore, the calculated adsorption energy values of -0.85 and -0.46 eV for Li-ion and Na-ion, respectively, indicate that Li/Na atom adsorption over monolayer TiC is a favorable process. The density of states plots show that after the adsorption of a single Li/Na atom, monolayer TiC maintains its metallic state, which is advantageous for the diffusion of stored electrons. Most remarkably, monolayer TiC exhibits energy densities of 2684 and 2015 mWh/g for Li and Na, respectively, which are significantly higher than commercial graphite and most other 2D anode materials. The fully loaded TiC anode exhibits excellent cycle stability with volume expansions as low as 0.13 and 0.11%, for Li and Na, respectively. Furthermore, an ultrafast diffusivity with low energy barriers of 0.02 and 0.10 eV is found in monolayer TiC for Li-ion and Na-ion, respectively, which suggests that it has an excellent charge/discharge capability. These exceptional properties make monolayer TiC an excellent candidate as an anode material for Li-ion and Na-ion batteries. Finally, SiC(111) has been proposed as a candidate substrate for monolayer TiC due to its minimal lattice mismatch.

Hybrid nodal surface and nodal line phonons in solids

Hybrid nodal surface and nodal line phonons in solids

Quantum nuclear delocalization and its rovibrational fingerprints.

Quantum mechanics dictates that nuclei must undergo some delocalization.In this work, emergence of quantum nuclear delocalization and its rovibrational fingerprints are discussed for the case of the van der Waals complex HHe3+.The equilibrium structure of HHe3+ is planar and T-shaped,one He atom solvating the quasi-linear He-H+-Hecore.The dynamical structure of HHe3+, in all of its bound states, isfundamentally different.As revealed by spatial distribution functions and nuclear densities, during thevibrations of the molecule the solvating He is not restricted to be in the planedefined by the instantaneously bent HHe3+ chomophore, but freely orbits the central proton, forming a three-dimensional torus around the HHe2+ chromophore.This quantum delocalization is observed for all vibrational states, the type ofvibrational excitation being reflected inthe topology of the nodal surfaces in the nuclear densities,showing, for example, that intramolecular bending involvesexcitation along the circumference of the torus.

Quantum Nuclear Delocalization and its Rovibrational Fingerprints

AbstractQuantum mechanics dictates that nuclei must undergo some delocalization. In this work, emergence of quantum nuclear delocalization and its rovibrational fingerprints are discussed for the case of the van der Waals complex . The equilibrium structure of is planar and T‐shaped, one He atom solvating the quasi‐linear He−H+−He core. The dynamical structure of , in all of its bound states, is fundamentally different. As revealed by spatial distribution functions and nuclear densities, during the vibrations of the molecule the solvating He is not restricted to be in the plane defined by the instantaneously bent chomophore, but freely orbits the central proton, forming a three‐dimensional torus around the chromophore. This quantum delocalization is observed for all vibrational states, the type of vibrational excitation being reflected in the topology of the nodal surfaces in the nuclear densities, showing, for example, that intramolecular bending involves excitation along the circumference of the torus.

Observation of flat band, Dirac nodal lines and topological surface states in Kagome superconductor CsTi3Bi5

Kagome lattices of various transition metals are versatile platforms for achieving anomalous Hall effects, unconventional charge-density wave orders and quantum spin liquid phenomena due to the strong correlations, spin-orbit coupling and/or magnetic interactions involved in such a lattice. Here, we use laser-based angle-resolved photoemission spectroscopy in combination with density functional theory calculations to investigate the electronic structure of the newly discovered kagome superconductor CsTi3Bi5, which is isostructural to the AV3Sb5 (A = K, Rb or Cs) kagome superconductor family and possesses a two-dimensional kagome network of titanium. We directly observe a striking flat band derived from the local destructive interference of Bloch wave functions within the kagome lattice. In agreement with calculations, we identify type-II and type-III Dirac nodal lines and their momentum distribution in CsTi3Bi5 from the measured electronic structures. In addition, around the Brillouin zone centre, {{mathbb{Z}}}_{2} nontrivial topological surface states are also observed due to band inversion mediated by strong spin-orbit coupling.