Nodal Lines Research Articles

Topological states in the polymerized carbon nanotubes

In this work, we report by ab initio calculations a systematical study on the energetic, dynamical, and electronic properties of polymerized (2n+1,0) (n=2,3,4) sing wall carbon nanotubes, termed as CNT(5,0), CNT(7,0), and CNT(9,0) carbon. The total energy calculations show that the equilibrium energies of the three carbon allotropes are lower than or comparable to the previously proposed bct-C16, bco-C16, and ors-C16 carbon. Their dynamical stabilities have been confirmed with phonon band spectrum calculations and their thermal stabilities have been confirmed with ab initio molecular dynamics simulations. Despite their unified space group symmetries and similar bonding types, their electronic properties are distinct: CNT(5,0) and CNT(7,0) carbon are topological nodal line semimetals with nodal rings in kx=0 and kz=0 mirror planes respectively, while the CNT(9,0) carbon is a semiconductor. To understand their distinct electronic behaviors, we provide a systematical explanation from the real space crystalline structure perspective. Our work has enriched the family of carbon allotropes with exotic band topologies and provide insights for the relations between real space crystalline structures and momentum space band topologies.

Entanglement entropy as an order parameter for strongly coupled nodal line semimetals

Topological semimetals are a class of many-body systems exhibiting novel macroscopic quantum phenomena at the interplay between high energy and condensed matter physics. They display a topological quantum phase transition (TQPT) which evades the standard Landau paradigm. In the case of Weyl semimetals, the anomalous Hall effect is a good non-local order parameter for the TQPT, as it is proportional to the separation between the Weyl nodes in momentum space. On the contrary, for nodal line semimetals (NLSM), the quest for an order parameter is still open. By taking advantage of a recently proposed holographic model for strongly-coupled NLSM, we explicitly show that entanglement entropy (EE) provides an optimal probe for nodal topology. We propose a generalized c-function, constructed from the EE, as an order parameter for the TQPT. Moreover, we find that the derivative of the renormalized EE with respect to the external coupling driving the TQPT diverges at the critical point, signaling the rise of non-local quantum correlations. Finally, we show that these quantum information quantities are able to characterize not only the critical point but also features of the quantum critical region at finite temperature.

Regression analysis of data based on the method of least absolute deviations in dynamic estimation problems

The use of regression analysis in dynamic problems of system estimation requires a high-speed algorithm of model parameter determination. Moreover, the original data may have stochastic heterogeneity which entails the necessity of the estimates of model parameters be resistant to various data anomalies. However, stable estimation methods, including the least absolute deviations method, are significantly inferior to the parametric ones. The goal of the study is to describe a computationally efficient algorithm for implementing the method of least absolute deviations for dynamic estimation of regression models and to study its capabilities for solving practical problems. This algorithm is based on descending along nodal lines. In this case, instead of the values of the objective function, its derivative in the direction of descent is considered. The computational complexity of the algorithm is also reduced due to the use of the solution of the problem at the previous step as a starting point and efficient updating of observations in the current data sample. The external performance of the proposed dynamic version of the algorithm of gradient descent along nodal lines has been compared with the static version and with the least squares method. It is shown that the dynamic version of the algorithm of gradient descent along the nodal lines make it possible to bring the speed close to that of the least squares method for common practical situations and to use the proposed version in dynamic estimation problems for a wide class of systems.

Dumpyawnus hpungwanus gen. et sp. nov., the second genus and species of Katlasidae (Hemiptera: Fulgoromorpha: Fulgoridoidea) from mid-Cretaceous Kachin amber, northern Myanmar

The second genus and species of the planthopper family Katlasidae, Dumpyawnus hpungwanus gen. et sp. nov., is described from mid-Cretaceous Kachin (Burmese) amber. It can be definitely attributed to Katlasidae mainly based on its tegminal structure (e.g., costal area absent, clavus closed, tegmen widened at membrane, multiplied forked of ScP + RA, MP and CuA2, single CuA1, nodal line absent) and hind wing venation (e.g., ScP + RA, RP, MP and CuA with 3–5 terminals), but the new genus is clearly different from Katlasus Luo, Jiang et Szwedo, 2020, the type genus of Katlasidae, according to its wing venation (e.g., terminals of ScP + RA usually forked, MP with less terminals). The morphological features and placement of the new taxon are briefly discussed.

Topological nodal lines in bulk and monolayer W2O3I4

By means of first-principles calculations, we study the topological nontrivial electronic structures and lattice dynamics of bulk and monolayer ${\mathrm{W}}_{2}{\mathrm{O}}_{3}{\mathrm{I}}_{4}$. We find that both of them are nodal-line semimetals in the absence of spin-orbit coupling (SOC), in which the nodal lines are induced by the band inversion between conduction and valence bands contributed by W $d$ and I p orbitals. Moreover, ${\mathrm{W}}_{2}{\mathrm{O}}_{3}{\mathrm{I}}_{4}$ bulk and monolayer exhibit excellent mechanical and thermal stability. By studying the external field modulation of topological nodal lines without SOC effect in monolayer ${\mathrm{W}}_{2}{\mathrm{O}}_{3}{\mathrm{I}}_{4}$, we find that the nodal lines are extremely robust against the biaxial strain but destroyed under vertical electric field due to the breaking of horizonal mirror symmetry. It is studied that the SOC effect here is large and non-negligible, and after considering the SOC effect, ${\mathrm{W}}_{2}{\mathrm{O}}_{3}{\mathrm{I}}_{4}$ bulk and monolayer undergo change of topological state from a topological nodal-line semimetal to a topological insulator. Our work not only extends the member of inorganic three-dimensional and two-dimensional topological semimetals library but also provides a prototype material candidate to investigate the double nodal-line surface states.

(Digital Presentation) Internal Friction, Mechanical Spectroscopy in SiO2/Si Wafers

In this work, after X-ray and electron irradiation, the outcomes of the evaluation dynamic characteristics of interstitial atoms Sij , 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 structure defect density Nd and the depth of the broken layer hb , 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 hSiO2 ≈ 100 nm, his = 300÷500×103 nm, and diameter D = 60÷100×10-3 m to measure the structurally sensitive internal friction Q-1 . Measurement of the internal friction background Q-1 0 at harmonic frequencies f0 and f2 allowed us to experimentally determine the nodal lines of the oscillating disks.

Non-Abelian Frame Charge Flow in Photonic Media

In PT-symmetric systems, the notion of non-Abelian frame charges enables multiband topological characterization of degeneracies by examining the eigenvector-frame rotations. Interestingly, some features of these frame charges can be viewed as an analog of electric charges confined in conducting wires, only that they flow in momentum space along nodal lines. But different from electric charges, these frame charges are not integers, and non-Abelian signatures emerge when braiding between adjacent band nodal lines occurs, which flips the direction of the flow. In photonic systems, the photonic Γ point serves as the source or sink of such a frame charge flow due to a hidden braiding induced by the often-ignored electrostatic mode at zero frequency. This source naturally generates non-Abelian topological signatures in PT-symmetric photonic systems that can be identified even in ordinary dielectric media. We use biaxial photonic crystals as examples to show how complex nodal line configurations can be explained as the topological consequences of the frame charge flow from the Γ point to the Brillouin zone boundaries. Our results reveal that non-Abelian band topology is intrinsically manifested in general photonic systems, making them easily accessible platforms for exploring non-Abelian physics.6 MoreReceived 11 September 2022Accepted 7 April 2023DOI:https://doi.org/10.1103/PhysRevX.13.021024Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasMetamaterialsSymmetry protected topological statesTopological effects in photonic systemsAtomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Two superconducting states with broken time-reversal symmetry in FeSe1-xSx.

Iron-chalcogenide superconductors FeSe1-xSx possess unique electronic properties such as nonmagnetic nematic order and its quantum critical point. The nature of superconductivity with such nematicity is important for understanding the mechanism of unconventional superconductivity. A recent theory suggested the possible emergence of a fundamentally new class of superconductivity with the so-called Bogoliubov Fermi surfaces (BFSs) in this system. However, such an ultranodal pair state requires broken time-reversal symmetry (TRS) in the superconducting state, which has not been observed experimentally. Here, we report muon spin relaxation (μSR) measurements in FeSe1-xSx superconductors for 0 ≤ x ≤ 0.22 covering both orthorhombic (nematic) and tetragonal phases. We find that the zero-field muon relaxation rate is enhanced below the superconducting transition temperature Tc for all compositions, indicating that the superconducting state breaks TRS both in the nematic and tetragonal phases. Moreover, the transverse-field μSR measurements reveal that the superfluid density shows an unexpected and substantial reduction in the tetragonal phase (x > 0.17). This implies that a significant fraction of electrons remain unpaired in the zero-temperature limit, which cannot be explained by the known unconventional superconducting states with point or line nodes. The TRS breaking and the suppressed superfluid density in the tetragonal phase, together with the reported enhanced zero-energy excitations, are consistent with the ultranodal pair state with BFSs. The present results reveal two different superconducting states with broken TRS separated by the nematic critical point in FeSe1-xSx, which calls for the theory of microscopic origins that account for the relation between nematicity and superconductivity.

Polar hairs of mixed-parity nodal superconductors in Rarita-Schwinger-Weyl metals

Linearly dispersing Rarita-Schwinger-Weyl (RSW) fermions featuring two Fermi velocities are the key constituents of itinerant spin-3/2 quantum materials. When doped, RSW metals sustain two Fermi surfaces (FSs), around which one fully gapped $s$ wave and five mixed-parity local pairings can take place. The intraband components of four mixed-parity pairings support point nodes at the poles of two FSs, only around which long-lived quasiparticles live. For weak (strong) pairing amplitudes ($\mathrm{\ensuremath{\Delta}}$), gapless north and south poles belonging to the same (different) FS(s) get connected by polar hairs, one-dimensional line nodes occupying the region between two FSs. The remaining one, by contrast, supports four nodal rings in between two FSs, symmetrically placed about their equators, but only when $\mathrm{\ensuremath{\Delta}}$ is small. For large $\mathrm{\ensuremath{\Delta}}$, this paired state becomes fully gapped. The transition temperature and pairing amplitudes follow the BCS scaling. We explicitly showcase these outcomes for a rotationally symmetric RSW metal and contrast our findings when the system possesses an enlarged Lorentz symmetry and with those in spin-3/2 Luttinger materials.

Vibrations That Do Not Promote Vibronic Coupling Can Dominate Observed Lineshapes in Two-Dimensional Electronic Spectroscopy.

Impulsively generated wavepackets can report on vibronic couplings underlying ultrafast electronic relaxation. Coherence maps (CMs) in multidimensional spectroscopy resolve beating amplitudes of such wavepackets as two-dimensional contour maps. A precise understanding of how these wavepackets manifest spectroscopically is vital for unambiguously deciphering their mechanistic significance and establishing CMs as a powerful tool for guiding the synthetic design of functional vibronic couplings. Here we take a step in this direction. We establish physically distinct origins of recently reported apparent similarities between diagonal node-like CM lineshapes in bacteriochlorophyll monomers and multichromophoric photosynthetic reaction centers (RCs). The former arise when vibrational wavepackets survive on both ground and excited electronic states, while nodal lines in RCs arise when vibrational wavepackets that do not participate in energy transfer are coherently transferred to the acceptor. We resolve recent spectroscopic observations and illustrate new mechanistic insights gained by connecting microscopic interference between electronic relaxation pathways and observed CMs.

Anisotropic transport and multiple topology in quasi-one-dimensional ternary telluride NbNiTe5

Topological quantum materials, which feature nontrivial band topology, have been one of the most attractive research topics in condensed-matter physics in recent decades. The low-dimensional topologically nontrivial materials are especially appealing due to the rich implications for topological physics and the potential applications in next-generation spintronic devices. Here, we report the crystal growth, anisotropic magnetotransport, Hall effect, and quantum de Haas--van Alphen (dHvA) oscillations of a quasi-one-dimensional ternary telluride ${\mathrm{NbNiTe}}_{5}$. The pronounced dHvA oscillations under $H\ensuremath{\parallel}b$ reveal three major oscillation frequencies ${F}_{\ensuremath{\alpha}}=136.41\phantom{\rule{0.16em}{0ex}}\mathrm{T}, {F}_{\ensuremath{\beta}}=240.34\phantom{\rule{0.16em}{0ex}}\mathrm{T}$, and ${F}_{\ensuremath{\gamma}}=708.03$ T and the associated light effective masses of charge carriers. From the angular dependence of dHvA oscillations, we have revealed the identified frequencies exhibit anisotropic character, all of which arise from the holelike Fermi surface sheets formed by band 1 (${F}_{\ensuremath{\alpha}}$ and ${F}_{\ensuremath{\beta}}$) and band 2 (${F}_{\ensuremath{\gamma}}$) by comparing with the Fermi surface calculations. First-principles calculations demonstrate that ${\mathrm{NbNiTe}}_{5}$ is a candidate of multiple topological material. In addition to the nonsymmorphic symmetry-protected nodal lines and band inversion (anticrossing) induced topological surface states, a ladder of topological gaps with the coexistence of strong and weak topology and a series of induced topological surface states are also identified.

Coexistence of Dirac points and nodal chains in photonic metacrystal.

Gapless topological phases, i.e. topological semimetals, come in various forms such as Weyl/Dirac semimetals, nodal line/chain semimetals, and surface-node semimetals. However, the coexistence of two or more topological phases in a single system is still rare. Here, we propose the coexistence of Dirac points and nodal chain degeneracies in a judiciously designed photonic metacrystal. The designed metacrystal exhibits nodal line degeneracies lying in perpendicular planes, which are chained together at the Brillouin zone boundary. Interestingly, the Dirac points, which are protected by nonsymmorphic symmetries, are located right at the intersection points of nodal chains. The nontrivial Z2 topology of the Dirac points is revealed by the surface states. The Dirac points and nodal chains are located in a clean frequency range. Our results provide a platform for studying the connection between different topological phases.

The gas-liquid-Q-factor-inversion in MEMS plate resonators

We present a semi-numerical method for solving the dynamics of microplates in viscous fluids. The method is based on the Kirchhoff plate equation with a hydrodynamic force deduced from the Stokes equations. The equation of motion is solved with the Galerkin mode decomposition (GMD) using the vacuum vibrational modes of cantilevered microplates as the basis functions. We investigate the Q-factor of the vibrational modes of microplate-resonators in gases and liquids. In gases, the Euler–Bernoulli (EB) modes (modes with nodal lines only along the plate’s width) exhibit the lowest Q-factors, while non-EB modes exhibit the highest Q-factors. In liquids, the opposite is found. EB modes exhibit the highest Q-factors, and non-EB modes lower Q-factors. We name this opposite Q-factor pattern in gases and liquids the gas-liquid-Q-inversion (GL-Q-inversion). Experiments in water and air showed a Q-factor agreement with the GL-Q-inversion, and differences in Q-factor between simulation and experiments were below 25%. Further numerical analysis reveals the physical mechanism underlying the GL-Q-inversion in terms of the system’s stored and dissipated energy. The results and methods shown here will pave the way to efficiently exploit the two-dimensional vibrational modes of microplate-resonators to improve their performance in gaseous and liquid environments.

Robust three-dimensional type-II Dirac semimetal state in SrAgBi

Topological semimetals such as Dirac, Weyl or nodal line semimetals are widely studied for their peculiar properties including high Fermi velocities, small effective masses and high magnetoresistance. When the Dirac cone is tilted, exotic phenomena could emerge whereas materials hosting such states are promising for photonics and plasmonics applications. Here we present evidence that SrAgBi is a spin-orbit coupling-induced type-II three-dimensional Dirac semimetal featuring tilted Dirac cone at the Fermi energy. Near charge compensation and Fermi surface characteristics are not much perturbed by 7% of vacancy defects on the Ag atomic site, suggesting that SrAgBi could be a material of interest for observation of robust optical and spintronic topological quantum phenomena.

Dirac nodal line induced anomalous low-energy acoustic plasmons on beryllium (0001) surface

Beryllium is a simple hexagonal metal but exhibits anomalous low-energy acoustic plasmons on its (0001) surface, which are radically distinct from the conventional metal surface plasmons. Although the plasmons on Be(0001) have been extensively studied, the underlying mechanism remains elusive. Here, through first-principles calculations combined with model analysis, we unambiguously demonstrate that it is the topological Dirac nodal line induced surface states that result in the anomalous low-energy acoustic plasmons on Be(0001), rather than the commonly believed Shockley surface states. Our study not only clarifies the origin of the puzzling anomalous plasmons on Be(0001), but also provides a sound theoretical interpretation for the appearance of low-energy acoustic surface plasmons on the noble metal (111) surfaces. This work suggests that the topological nodal line semimetals offer a potential platform for obtaining low-energy acoustic plasmons.

Magnetotransport properties and Fermi surface topology of the nodal line semimetal InBi

In the present study, we have thoroughly characterized the 3D Fermi surface of a topological nodal line semimetal InBi via the Shubnikov--de Haas oscillations and density functional theory. The nitty-gritty of its full 3D Fermi surface has been discussed in detail. The Fermi surface topology and the Hall conductivity emphasized the carrier compensation as a driving force for the observed extremely high magnetoresistance. The magnetotransport revealed a unique magnetic-field-induced metal-semiconducting transition. The origin of such a phenomenon has been elaborated theoretically which has implications for layered topological nodal line semimetals with linearly dispersing bands.

Quantized thermoelectric Hall plateau in the quantum limit of graphite as a nodal-line semimetal

We performed thermoelectric Hall conductivity ${\ensuremath{\alpha}}_{xy}$ measurements on single-crystal graphite in the quantum limit up to 13 T. Both electrical and thermoelectric transport measurements were performed on the same crystal to extract pure ${\ensuremath{\alpha}}_{xy}$, avoiding any sample quality dependence. The ${\ensuremath{\alpha}}_{xy}$ converges to a plateau in the quantum limit with a linear dependence on temperature. This behavior is analogous to the quantized thermoelectric Hall effect (QTHE) observed in three-dimensional Dirac/Weyl nodal-point semimetals, and experimentally confirms a theoretical proposal on the QTHE in semimetals with nodal lines as in graphite.

Electronic structures near unmovable nodal points and lines in two-dimensional materials

Unmovable nodal points (UNPs) and lines (UNLs) are band crossings whose positions in the Brillouin zone are unaltered by symmetry preserving perturbations. Not only positions but also the band structure in their vicinity are determined by the little group of wave vectors and its irreducible (co)representations. In this paper, we give the full set of electronic dispersions near all UNPs and UNLs in non-magnetic quasi two-dimensional (2D) materials, both with and without spin–orbit coupling (SOC). Analysis of all layer gray single and double groups gives nineteen different quasiparticles, the great majority of which are unavoidable for a 2D material that belongs to a certain layer group. This includes Weyl and Dirac nodal lines, dispersions with quadratic or cubic splitting, anisotropic Weyl and Dirac cones, whose orientation can be varied by e.g. strain etc. We indicated quasiparticles that are robust to SOC. For convenience, our results are concisely presented graphically—as a map, not in a tabular, encyclopedia form. They may be of use as checkpoints and/or for fitting experimentally (via e.g. ARPES) and numerically obtained electronic band structures data, as well as for deeper theoretical investigations.

Topological semimetal phases in a family of monolayer X3YZ6 (X=Nb,Ta, Y=Si,Ge,Sn, Z=S,Se,Te) with abundant nodal lines and nodes

The electronic and topological properties of single-layer X3YZ6 (X=Nb,Ta, Y=Si,Ge,Sn, Z=S,Se,Te) materials have been studied with the aid of first principles calculations. This kind of materials belong to topological semimetals (TMs) with abundant nodal lines and nodes. Considering their similar properties, we focus on the analysis of Ta3SnTe6 and Ta3SiSe6. The presence of spin–orbit coupling (SOC) leads to the transition from type-I nodal lines to Dirac points as well as the disappear of type-II Dirac points. The three-dimensional (3D) plot of the band structure reproduces vividly the characteristics of nodes and nodal lines. The appearance of the flat bands in (110) edge states further confirm their nontrivial topological properties. We also explore the relationship among different nodal lines (nodes), crystal symmetry and SOC. The type-I nodal lines are protected by Mz and Mỹ symmetry in the absence of SOC. Symmetry breaking leads to band splitting even in the presence of SOC. The single-layer X3YZ6 can be used as candidates for two-dimensional (2D) Dirac materials and provide a platform for further study of interesting physical phenomena.

Type‐II Dirac Nodal Lines in a Double‐Kagome‐Layered Semimetal

AbstractLorentz‐violating type‐II Dirac nodal line semimetals (DNLSs), hosting curves of band degeneracy formed by two dispersion branches with the same sign of slope, represent a novel state of matter. While being studied extensively in theory, convincing experimental evidence of type‐II DNLSs remain elusive. Recently, vanadium‐based kagome materials have emerged as a fertile ground to study the interplay between lattice symmetry and band topology. This work studies the low‐energy band structure of double‐kagome‐layered CsV8Sb12 and identifies it as a scarce type‐II DNLS protected by mirror symmetry. This work observes multiple DNLs consisting of type‐II Dirac cones close to or almost at the Fermi level via angle‐resolved photoemission spectroscopy (ARPES), which provides an electronic explanation for the nonsaturating magnetoresistance effect as observed. First‐principles theory analyses show that spin‐orbit coupling only opens a small gap, resulting in effectively gapless ARPES spectra, yet generating large spin Berry curvature. These type‐II DNLs, together with the interaction between a low‐energy van Hove singularity and quasi‐one‐dimensional band as observed in the same material, suggest CsV8Sb12 as an ideal platform for exploring novel transport properties.