Nodal Lines Research Articles

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.

Experiments on symmetry breaking of azimuthal combustion instabilities and their analysis combining acoustic energy balance and flame describing functions

Combustion instabilities in annular systems raise fundamental issues that are also of practical importance to aircraft engines and ground-based gas turbine combustors. Recent studies indicate that the injector plays a significant role in the stability of combustors by defining the flame dynamical response and setting the inlet impedance of the system. The present investigation examines the effects of combinations of injectors of two different types ( $U$ and $S$ ) on thermoacoustic instabilities in a laboratory-scale annular combustor and compares different circumferential staging strategies. The combustor operates in a stable fashion when all injection units belong to the $S$ -family, but exhibits large amplitude pressure oscillations when all these units are of the $U$ -type. When the system comprises a mix of $U$ - and $S$ -injectors, it is possible to determine the number of $S$ -injectors leading to stable operation. For a fixed proportion of $U$ - and $S$ -injectors, some arrangements give rise to stable operation while others do not. Results also show that introducing symmetry-breaking elements affects the system's modal dynamics. These experimental observations are interpreted in an acoustic energy balance framework used to derive an expression for the growth rate as a function of the describing functions of the flames formed by the different injectors and their respective azimuthal locations. Growth rates are determined for the different configurations and used to explain the various observations, estimate the system damping rate and predict the location of the nodal line when the standing mode prevails.

Double Dirac nodal lines enforced by multiple nonsymmorphic symmetries

Double Dirac nodal lines enforced by multiple nonsymmorphic symmetries

Engineering Two-Dimensional Nodal Semimetals in Functionalized Biphenylene by Fluorine Adatoms.

We propose a band engineering scheme on the biphenylene network, a newly synthesized carbon allotrope. We illustrate that the electronic structure of the biphenylene network can be significantly altered by controlling conditions affecting the symmetry and destructive interference of wave functions through periodic fluorination. First, we investigate the mechanism for the appearance of a type-II Dirac fermion in a pristine biphenylene network. We show that the essential ingredients are mirror symmetries and stabilization of the compact localized eigenstates via destructive interference. While the former is used for the band-crossing point along high symmetry lines, the latter induces highly inclined Dirac dispersions. Subsequently, we demonstrate the transformation of the biphenylene network's type-II Dirac semimetal phase into various Dirac phases such as type-I Dirac, gapped type-II Dirac, and nodal line semimetals through the deliberate disruption of mirror symmetry or modulation of destructive interference by varying the concentration of fluorine atoms.

Nonsymmorphic symmetry protected nodal lines in layered topological semimetal Ta3GeTe6

Topological semimetals have garnered significant attention due to their distinctive physical properties. However, the ideal material platforms for studying these phenomena remain limited. Here, we report the synthesis and nontrivial topological properties of high-quality van der Waals material Ta3GeTe6. Angle-resolved photoemission spectroscopy studies performed systematically on the as-grown Ta3GeTe6 single crystal along different high-symmetry directions reveal the formation of two nodal lines located near 0.07 and 0.55 eV below EF along the loop X-U-R-S, which arises from band crossings protected by nonsymmorphic symmetry. Furthermore, the nodal lines near the Fermi level along the S-R and S-X directions exhibit a flat feature. The discovery of this material enriches the family of topological nodal line semimetals and provides a promising platform for future investigations into exotic electronic correlation phenomena and potential device applications.

Dynamic Management of Flexibility in Distribution Networks through Sensitivity Coefficients

Due to a rising share of renewable energy sources on the production side and electrification of transport and heating on the consumption side, the efficient management of flexibility in distribution networks is crucial for ensuring optimal operation and utilization of resources. Nowadays, the sensitivity-based approach is mainly used in medium-voltage (MV) networks for regulating voltage profiles with reactive power of distributed energy resources (DER). The main disadvantage of the simplified sensitivity-based method is its inaccuracy in case of a high deviation of the network voltage from the nominal values. Furthermore, it was also noted that despite the fact that the method is well described in the literature, there is a lack of systematic approach to its implementation in real-life applications. Thus, the main objective of this paper is to address this disadvantage and to propose an algorithm designed to calculate required consumer flexibility in near real-time to ensure distribution grid operation within operational criteria. In the first part of the paper, network state, including line loading and node voltages, is assessed to determine distribution network node capacity. By analyzing the sensitivity of network busbars to changes in consumption and production, our algorithm effectively identifies the most efficient nodes and facilitates strategic decision-making for resource allocation. We demonstrate the effectiveness of our approach through simulations of real-world distribution network data, highlighting its ability to enhance network flexibility and improve resource utilization. Leveraging sensitivity coefficients, the algorithm enables flexible consumption and production management across various scenarios, supporting the transition to a more dynamic and efficient power system.

Symmetric/Asymmetric Vibrational Characteristics of Bi-Directional Functionally Graded Annular Microplates

In this study, a free vibration model of bi-directional functionally graded (BD-FG) annular microplates is established based on the modified couple stress theory (MCST) and the first-order shear deformation theory (FSDT), and the corresponding governing equations are derived from Hamilton’s principle. The annular microplates are assumed to be composed of metal and ceramic materials, and the equivalent material properties are a combination of power-law function and exponential ones. The generalized differential quadrature method (GDQM) is used to obtain the vibration frequencies and mode displacements for the C–C, S–C, C–S, and S–S (S: simply supported; C: clamped) annular microplates. The convergence and validity of the proposed model are verified through selective numerical examples. Further, the effects of gradient index, material length scale parameter, boundary conditions, and geometrical dimensions on the symmetric/asymmetric vibration frequencies of the annular microplate are explored. The modal assurance criterion is applied to estimate the influence of the radial gradient index and material length scale parameter on different-order mode displacements of the annular microplate. The results show that: (1) the vibration frequencies of the annular microplate are sensitive to changes in the geometry and boundary conditions; (2) compared with the axial gradient index, the radial gradient index not only affects the vibration frequencies of the annular microplate, but also impacts the distribution of the highest and lowest points of the vibration mode displacements as well as the vibration mode nodal lines; (3) as the material length scale parameter increases, the vibration frequencies are significantly increased, and the higher-order vibration modes of the annular microplate also change.

Experimental investigation of high-frequency transverse instability in Helmholtz resonator-coupled lean-premixed hydrogen combustor

Recent experimental studies suggest that lean-premixed pure hydrogen combustion plays a central role in generating self-sustained pressure oscillations, preferentially coupled with high-frequency tangential modes in land-based gas turbine combustors. The triggering of such high-frequency combustion dynamics is known to be closely connected with relatively small, flashback-resistant, characteristic nozzle dimensions, and the structural and kinematic properties of the premixed hydrogen flames. To identify important trends in the transverse modal dynamics of hydrogen flames, here we conduct detailed measurements of multislit injector-driven hydrogen flame dynamics. We analyze the measured data using the wave decomposition technique for PDF-based statistical assessments of bimodality and nodal line orientation. Experimentally, the planar-to-transverse mode transformation is revealed to be controlled by the combined influence of flame temperature and thermal power, which ultimately leads to the development of well-defined standing modes at around 4.69 kHz under the most severe test condition. Using analytic modeling and rigorous validation measurements, we also investigate Helmholtz resonator-type passive stabilization and its impact on the integrated system's thermoacoustic states with respect to the change in purge air flowrate. Our results show that the coupled system does not retain many of the initial thermoacoustic properties, but instead undergoes prominent changes in the first tangential modal dynamics, progressively evolving from a large-amplitude bimodal to a low-amplitude unimodal state.

Anelastic Internal Friction and Mechanical Spectroscopy of SiO2/Si Wafers

In this work, after electron irradiation and X-ray, the outcomes of the evaluation dynamic characteristics of interstitial atoms Si j , vacancy V, and O-complexes were evaluated to account for the annealing conditions to derive specific structural defects in the SiO2/Si wafer. A non-destructive method, which allows the determination of the internal friction difference ΔQ −1 /Q −1 0 of the elastic vibration of structural defects of dislocations with density N D and the depth of the broken layer h b , is offered for the SiO2/Si wafer. The method was developed, the installation was designed and manufactured for the excitation and registration of damped bending resonant oscillations in a SiO2/Si disc-shaped wafer with a thickness h SiO2 ≈ 100 nm, h is = 300 ÷ 500 × 103 nm, and diameter D = 60 ÷ 100 × 10−3 m to measure the structurally sensitive internal friction Q −1 in vacuum P ≈ 10−2 Pa. Measurement of the internal friction background Q −1 0 at harmonic frequencies f 0 and f 2 allowed us to experimentally determine the nodal lines of the oscillating disks.

Hyperbolic metamaterial empowered controllable photonic Weyl nodal line semimetals

Motivated by unique topological semimetals in condensed matter physics, we propose an effective Hamiltonian with four degrees of freedom to describe evolutions of photonic double Weyl nodal line semimetals in one-dimensional hyper-crystals, which supports the energy bands translating or rotating independently in the form of Weyl quasiparticles. Especially, owing to the unit cells without inversion symmetry, a pair of reflection-phase singularities carrying opposite topological charges emerge near each nodal line, and result in a unique bilateral drumhead surface state. After reducing radiation leakages and absorption losses, these two singularities gather together gradually, and form a quasi-bound state in the continuum (quasi-BIC) ring at the nodal line ultimately. Our work not only reports the first realization of controllable photonics Weyl nodal line semimetals, establishes a bridge between two independent topological concepts−BICs and Weyl semimetals, but also heralds new possibilities for unconventional device applications, such as dual-mode schemes for highly sensitive sensing and switching.

Reversible non-volatile electronic switching in a near-room-temperature van der Waals ferromagnet

Non-volatile phase-change memory devices utilize local heating to toggle between crystalline and amorphous states with distinct electrical properties. Expanding on this kind of switching to two topologically distinct phases requires controlled non-volatile switching between two crystalline phases with distinct symmetries. Here, we report the observation of reversible and non-volatile switching between two stable and closely related crystal structures, with remarkably distinct electronic structures, in the near-room-temperature van der Waals ferromagnet Fe5−δGeTe2. We show that the switching is enabled by the ordering and disordering of Fe site vacancies that results in distinct crystalline symmetries of the two phases, which can be controlled by a thermal annealing and quenching method. The two phases are distinguished by the presence of topological nodal lines due to the preserved global inversion symmetry in the site-disordered phase, flat bands resulting from quantum destructive interference on a bipartite lattice, and broken inversion symmetry in the site-ordered phase.

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.

Chemical-substitution-driven giant anomalous Hall and Nernst effects in magnetic cubic Heusler compounds

Chemical substitution efficiently optimizes the physical properties of Heusler compounds, especially their anomalous transport properties, including anomalous Hall conductivity (AHC) and anomalous Nernst conductivity (ANC). This study systematically investigates the effect of chemical substitution on AHC and ANC in 1493 magnetic cubic Heusler compounds using high-throughput first-principles calculations. Notable trends emerge in Co- and Rh-based compounds, where chemical substitution effectively enhances the AHC and ANC. Intriguingly, certain chemically substituted candidates exhibit outstanding enhancement in AHCs and ANCs, such as (Co0.8Ni0.2)2FeSn with considerable AHC and ANC values of −2567.78 Scm−1 and 8.27 Am−1K−1, respectively, and (Rh0.8Ru0.2)2MnIn with an AHC of 1950.49 Scm−1. In particular, an extraordinary ANC of 8.57 Am−1K−1 is identified exclusively in Rh2Co0.7Fe0.3In, nearly double the maximum value of 4.36 Am−1K−1 observed in the stoichiometric Rh2CoIn. A comprehensive band structure analysis underscores that the notable enhancement in ANC arises from the creation and modification of the energy-dependent nodal lines through chemical substitution. This mechanism generates a robust Berry curvature, resulting in significant ANCs. These findings emphasize the pivotal role of chemical substitution in engineering high-performance materials, thereby expanding the horizons of transport property optimization within Heusler compounds.

Stability of 2D Crystals from Tessellation

AbstractReticular chemistry has been a cornerstone in the design of novel 2D materials. Despite numerous possibilities for topological arrangements, only a few with high symmetry can form stable networks. Here, starting from 2D carbons, four types of highly stable tessellations are discovered, which consist of chains of non‐hexagonal rings separated by hexagonal ribbons. A modified Read–Shockley model is established to perfectly describe the stability of these highly stable frameworks, which is based on the interaction between non‐hexagonal rings. Moreover, these four types of tessellations and the modified Read–Shockley model are found to be of general validity in designing highly stable 2D materials, which is verified by the calculations on polymorphs of boron nitride and molybdenum disulfide. Besides, among the studied 2D carbon allotropes, two semi‐metallic structures with highly anisotropic Dirac cones and one semimetal with a Dirac nodal line at the Fermi level are discovered, as protected by their D2h symmetry. Spin‐orbital coupling is further found to open small bandgaps for these three Dirac structures, making them nontrivial topological insulators. The in‐depth understanding of the stability of 2D crystals in this study provides a new way for rational design of 2D crystals that may show peculiar electronic structures.

Exploration of Resonant Modes for Circular and Polygonal Chladni Plates.

In general, sound waves propagate radially outwards from a point source. These waves will continue in the same direction, decreasing in intensity, unless a boundary condition is met. To arrive at a universal understanding of the relation between frequency and wave propagation within spatial boundaries, we explore the maximum entropy states that are realized as resonant modes. For both circular and polygonal Chladni plates, a model is presented that successfully recreates the nodal line patterns to a first approximation. We discuss the benefits of such a model and the future work necessary to develop the model to its full predictive ability.

Twist-Angle Tuning of Electronic Structure in Two-Dimensional Dirac Nodal Line Semimetal Au2Ge on Au(111).

Topological semimetals have emerged as quantum materials including Dirac, Weyl, and nodal line semimetals, and so on. Dirac nodal line (DNL) semimetals possess topologically nontrivial bands crossing along a line or a loop and are considered precursor states for other types of semimetals. Here, we combine scanning tunneling microscopy/spectroscopy (STM/S) measurements and density functional theory (DFT) calculations to investigate a twist angle tuning of electronic structure in two-dimensional DNL semimetal Au2Ge. Theoretical calculations show that two bands of Au2Ge touch each other in Γ-M and Γ-K paths, forming a DNL. A significant transition of electronic structure occurs by tuning the twist angle from 30° to 24° between monolayer Au2Ge and Au(111), as confirmed by STS measurements and DFT calculations. The disappearing of DNL state is a direct consequence of symmetry breaking.

An analytical model for the analysis of vibration and energy flow in a clamped stiffened plate using integral transform technique

Based on Kirchhoff thin plate and Mindlin thick plate theories, the vibration and energy flow characteristics of clamped stiffened plate are studied by using the analytical model constructed by finite integral transform method. The results show that the energy flow characteristics of the stiffened plate at the beam/plate coupling interface depend on the position of the rib in the vibration modes of the plate. The effects of shear deformation and rotatory inertia on the energy flow across the beam/plate coupling interface of the stiffened plate are further investigated. It is found that the inclusion of rotatory inertia of the beam and plate in the model only affects the energy flow component controlled by the moment coupling but not that controlled by the shear force coupling. Whilst the inclusion of the shear deformation of the beam and plate mainly causes a decreased amplitude of the energy flow for the mode group where the beam is located away from both the nodal and antinodal lines of modes, in addition to the shear deformation of the plate which also leads to an increased amplitude of the energy flow component controlled by the shear force coupling for the mode group where the beam locates at the antinodal line of modes. The understanding of energy flow characteristics of the stiffened plate at the beam/plate interface is essential to effectively control the noise and vibration problems of structures such as transformer tanks and machine covers.

Measuring the internal damping of thin metal beams in flexure

Since the internal damping of most metals is a relatively small quantity, precise measurement requires that both acoustic radiation damping and boundary condition damping be either eliminated or highly minimized. In this talk, an experiment setup will be described which can measure the internal damping of metal beams in flexure. To perform a measurement, a beam specimen is placed on wire supports within a vacuum chamber and excited by an autonomous force hammer located within the chamber. The wire supports are located exactly at the nodal lines of the beam mode of interest, so that the frictional losses created by the wire supports are minimized. Once excited, the beam deflection is measured with a single point laser vibrometer. The signal decay measured by the vibrometer is used to estimate damping of the mode of interest using either the Hilbert transform or the half- power method. The wire supports are then moved, and the procedure is repeated for the next mode of interest. Results for several metal specimens will be presented and compared to Zener’s thermoelastic model, which describes the losses created by thermal currents for a beam in flexure, to demonstrate the accuracy of the measurement method.

Nontrivial Topological Phases in Ternary Borides M2XB2 (M=W, Mo; X=Co, Ni)

The nontrivial band topologies protected by certain symmetries have attracted significant interest in condensed matter physics. The discoveries of nontrivial topological phases in real materials provide a series of archetype materials to further explore the topological physics. Ternary borides M2XB2 (M = W, Mo; X = Co, Ni) have been widely investigated as the wear-resistant and high-hardness materials. Based on first-principles calculations, we find the nontrivial topological properties in these materials. Taking W2NiB2 as an example, this material shows the nodal line semimetal state in the absence of spin-orbit coupling. Two types of nodal lines appear near the Fermi level simultaneously. One is protected by the combined space-inversion and time-reversal symmetry, and the other is by the mirror symmetry. Part of these two-type nodal lines form nodal chains. When spin-orbit coupling is included, these nodal lines are fully gapped and the system becomes a strong topological insulator with nontrivial Z 2 index (1;000). Our calculations demonstrate that a nontrivial spin-momentum locked surface Dirac cone appears on the (1¯10) surface. We also find that other isostructural ternary borides Mo2NiB2, Mo2CoB2, and W2CoB2 possess similar topological band structures. Therefore, our work not only enriches the understanding of band topology for ternary borides, but also lays the foundation for the further study of topological phases manipulation and potential spintronic applications in realistic materials.

Topological phase transition and surface states in a non-Abelian charged nodal line photonic crystal

Abstract Topological charges of nodal lines in a multigap system are represented by non-Abelian numbers, and the Euler class, a topological invariant, can be used to explain their topological phase transitions, such as pair-annihilation of nodal lines. Up until now, no discussion of phase transitions of nodal lines in photonic crystals using the Euler class has been reported, despite the fact that the Euler class and topological phase transition have recently been addressed in metallic or acoustic crystals. Here, we show how the deformation of a photonic crystal causes topological phase transitions in the nodal lines, and the Euler class can be used to theoretically predict the nodal lines’ stability based on the non-Abelian topological charge theory. Specifically, by manipulating the separation between the two single diamond structures and the extent of structural distortion, we numerically demonstrate the topological transition of nodal lines, e.g., from nodal lines to nodal rings. We then demonstrate that the range of surface states is strongly influenced by the topological phase transition of nodal lines. Moreover, the Zak phase was used to explain the surface states’ existence.