Nodal Structure Research Articles

Topological characteristics of gap closing points in nonlinear Weyl semimetals

In this work we explore the effects of nonlinearity on three-dimensional topological phases. Of particular interest are the so-called Weyl semimetals, known for their Weyl nodes, i.e., point-like topological charges which always exist in pairs and demonstrate remarkable robustness against general perturbations. It is found that the presence of onsite nonlinearity causes each of these Weyl nodes to break down into nodal lines and nodal surfaces at two different energies while preserving its topological charge. Depending on the system considered, additional nodal lines may further emerge at high nonlinearity strength. We propose two different ways to probe the observed nodal structures. First, the use of an adiabatic pumping process allows the detection of the nodal lines and surfaces arising from the original Weyl nodes. Second, an Aharonov-Bohm interference experiment is particularly fruitful to capture additional nodal lines that emerge at high nonlinearity.

Infrared plasmons propagate through a hyperbolic nodal metal.

Metals are canonical plasmonic media at infrared and optical wavelengths, allowing one to guide and manipulate light at the nanoscale. A special form of optical waveguiding is afforded by highly anisotropic crystals revealing the opposite signs of the dielectric functions along orthogonal directions. These media are classified as hyperbolic and include crystalline insulators, semiconductors, and artificial metamaterials. Layered anisotropic metals are also anticipated to support hyperbolic waveguiding. However, this behavior remains elusive, primarily because interband losses arrest the propagation of infrared modes. Here, we report on the observation of propagating hyperbolic waves in a prototypical layered nodal-line semimetal ZrSiSe. The observed waveguiding originates from polaritonic hybridization between near-infrared light and nodal-line plasmons. Unique nodal electronic structures simultaneously suppress interband loss and boost the plasmonic response, ultimately enabling the propagation of infrared modes through the bulk of the crystal.

Charge Transport Across Dynamic Covalent Chemical Bridges.

Relationships between chemical structure and conductivity in ordered polymers (OPs) are difficult to probe using bulk samples. We propose that conductance measurements of appropriate molecular-scale models can reveal trends in electronic coupling(s) between repeat units that may help inform OP design. Here, we apply the scanning tunneling microscope-based break-junction (STM-BJ) method to study transport through single-molecules comprising OP-relevant imine, imidazole, diazaborole, and boronate ester dynamic covalent chemical bridges. Notably, solution-stable boron-based compounds dissociate in situ unless measured under a rigorously inert glovebox atmosphere. We find that junction conductance negatively correlates with the electronegativity difference between bridge atoms, and corroborative first-principles calculations further reveal a different nodal structure in the transmission eigenchannels of boronate ester junctions. This work reaffirms expectations that highly polarized bridge motifs represent poor choices for the construction of OPs with high through-bond conductivity and underscores the utility of glovebox STM-BJ instrumentation for studies of air-sensitive materials.

Unremovable linked nodal structures protected by crystalline symmetries in stacked bilayer graphene with Kekulé texture

Linking structure is a new concept characterizing topological semimetals, which indicates the interweaving of gap-closing nodes at the Fermi energy ($E_F$) with other nodes below $E_F$. As the number of linked nodes can be changed only via pair-creation or pair-annihilation, a linked node is more stable and robust than ordinary nodes without linking. Here we propose a new type of a linked nodal structure between a nodal line (nodal surface) at $E_F$ with another nodal line (nodal surface) below $E_F$ in two-dimensional (three-dimensional) spinless fermion systems with $\mathcal{IT}$ symmetry where $\mathcal{I}$ and $\mathcal{T}$ indicate inversion and time-reversal symmetries, respectively. Because of additional chiral and rotational symmetries, in our system, a double band inversion creates a pair of linked nodes carrying the same topological charges, thus the pair are unremovable via a Lifshiftz transition, which is clearly distinct from the cases of the linked nodes reported previously. A realistic tight binding model and effective theory are developed for such a linking structure. Also, using density functional theory calculations, we propose a class of materials, composed of stacked bilayer graphene with Kekul\'{e} texture, as a candidate system hosting the new type of the linked nodal structure.

Anomalous Nernst effect in the nonmagnetic nodal-line semimetal PbTaSe2

PbTaSe$_2$ is a unique topological material, in which the number of nodal lines is expected to change at the structural transition between the lower temperature/pressure "L" phase and the higher temperature/pressure "H" phase. We report the anomalous Nernst effect attributed to the Berry curvature of nodal lines and its change with the structural transition. In the L phase, the Nernst coefficient ($S_{yx}$) shows the step-like magnetic field dependence reminiscent of the anomalous Nernst effect of nonmagnetic Dirac/Weyl semimetals. By applying hydrostatic pressure, we discovered that the amplitude of the anomalous component significantly decreases at the transition to the H phase, which might correspond to the partial annihilation of nodal line structures.

A REVIEW IN NODAL ANATOMY FOR PLANTS

Nodal anatomy reveals the number, behavior and fait of bundles in each node and internode. Firstly, three main types of nodes represented by the one trace- one gap, the three trace- three-gaps, and the multi-traces- multi gaps in plants were proposed. Then the fourth types of nodes, represented by two- multi traces - one gap , was added to nodal types, while the fifth type (split –lateral) has been proposed, where a single trace associated with numerous leaves by splitting as found in different families from Angiosperms.Branches traces are distinct from leaf ones, and it represented of one or several bundles formed in axillary of leaves, commonly branch trace and middle leaf trace formed with the same gab,One of the important facts of studying nodal anatomy is the relationship between nodal structure and leaf base referring to stipules and sheathing base as well as the phyllotaxy. In monocot plants leaves characterized by sheathing bases, So the leaves nodes appeared with numerous leaf traces separated from different stem bundles, in Dicots plant different nodal types recognized.the studies of nodal anatomy are considered as an important features in taxonomical studies and phylogenetic studies on Dicots plant, most the studies revealed the di-traces and tri-traces nodes considered as primitive type while the uni-trace or multi-traces node are the advanced and it was proposed either by reduction or amplification.

Technique to match mesorectal lymph nodes imaging findings to histopathology: node-by-node comparison.

Lymph node status is critical for staging rectal cancer and determining neoadjuvant therapy regimens. Establishing a matching between imaging and histopathological lymph nodes is fundamental for predicting lymph node status. This study reports a technique to achieve node-by-node pairing of mesorectal lymph nodes between imaging findings and histopathology. Fifty-two patients with histopathologically verified rectal cancer underwent magnetic resonance imaging before surgery. The status of each lymph node in the surgical specimens was analyzed histopathologically and matched with preoperative imaging after the operation. A total of 346 mesorectal lymph nodes were located on imaging evaluation, of which 313 were confirmed histopathologically, and 33 were unmatched. The total success rate of the technique was 90.5%. Node-by-node analysis revealed 280 benign and 33 malignant nodal structures. The technique to match mesorectal lymph node imaging findings to histopathology was feasible and effective. It simplified the technical method and had a reasonable success matching rate, which could provide a standardized approach for obtaining a prospective correlation between imaging and histological findings, supporting all subsequent related studies at the level of mesorectal lymph nodes.

Triple nodal points characterized by their nodal-line structure in all magnetic space groups

Triple nodal points are threefold degeneracies of energy bands in momentum space and therefore constitute intermediates between Dirac and Weyl points. Here, the authors study these band nodes in spinless band structures arising in any space group, possibly magnetic and nonsymmorphic, and derive a complete symmetry classification according to the nodal-line structure in the vicinity of the triple nodal point. This provides criteria for the stability of such band nodes and predicts the intricate nodal structures observed in data obtained by first-principles calculations for real materials.

Surrogate modeling of parametrized finite element simulations with varying mesh topology using recurrent neural networks

A machine learning based strategy is proposed for creating parametric surrogate models from parametrized finite element model simulation results. In the first major step, a unified nodal data structure is created from the topologically inhomogeneous set of finite element simulations. This is achieved by utilizing re-sampling and the coherent point drift method for node registration of the different designs. In the second major step, a parametric surrogate model is trained for predicting the initial coordinates using a fully-connected feed-forward neural network. Two different recurrent neural network modeling approaches are presented and compared for the prediction of various field quantities with different degrees of complexity and non-linearity. For the first proposed modeling approach, a node-by-node prediction is applied, where the time series of each structural node is predicted independently via a compact long-short term memory (LSTM) model. For each node, the initial coordinates of the node are used as additional input features. For the second modeling approach, an all-at-once prediction is applied, where the time series of all structural nodes are predicted at once by training an LSTM model on a reduced output space obtained by principal component analysis (PCA). Output fields exhibiting moderate non-linearity could be well predicted by both approaches, but only the node-by-node approach allowed an accurate generalized representation of a strongly non-linear and narrow field quantity representing the observed crack patterns within the finite element structure. The existence of a new yet unobserved crack pattern could be identified by the node-by-node approach and confirmed by subsequently running the corresponding FE simulation.

Feather characteristics of Common Myna Acridotheres tristis (Passeriformes: Sturnidae) from India

The systematic study of feather microstructure supports species identification, which is important in cases of illegally traded birds and bird-aircraft strikes. Our study focused on morphometric, macro- and micro-characters of feathers of Common Myna Acridotheres tristis from India. Among macro-characters, silver-colored filoplume feathers with pale black pigmentation on the barbs are specific for A. tristis. Morphometric measurements revealed that primary contour feathers (10.8±0.100 cm) were the longest and bristle feathers (1.26±0.051 cm) the shortest among all feathers. The longest (average) barb is found in primary contour feathers (1.875±0.123 cm), and the shortest in filoplume feathers (0.288±0.017 cm). We observed 3 types of nodal structures, and elongated prongs in bristle and filoplume feathers are significant characteristics of A. tristis. These insights into feather microstructures of A. tristis will aid species identification using plumology.

Validating visual evoked potentials as a preclinical, quantitative biomarker for remyelination efficacy.

Many biomarkers in clinical neuroscience lack pathological certification. This issue is potentially a significant contributor to the limited success of neuroprotective and neurorestorative therapies for human neurological disease-and is evident even in areas with therapeutic promise such as myelin repair. Despite the identification of promising remyelinating candidates, biologically validated methods to demonstrate therapeutic efficacy or provide robust preclinical evidence of remyelination in the CNS are lacking. Therapies with potential to remyelinate the CNS constitute one of the most promising and highly anticipated therapeutic developments in the pipeline to treat multiple sclerosis and other demyelinating diseases. The optic nerve has been proposed as an informative pathway to monitor remyelination in animals and human subjects. Recent clinical trials using visual evoked potential have had promising results, but without unequivocal evidence about the cellular and molecular basis for signal changes on visual evoked potential, the interpretation of these trials is constrained. The visual evoked potential was originally developed and used in the clinic as a diagnostic tool but its use as a quantitative method for assessing therapeutic response requires certification of its biological specificity. Here, using the tools of experimental pathology we demonstrate that quantitative measurements of myelination using both histopathological measures of nodal structure and ultrastructural assessments correspond to visual evoked potential latency in both inflammatory and chemical models of demyelination. Visual evoked potential latency improves after treatment with a tool remyelinating compound (clemastine), mirroring both quantitative and qualitative myelin assessment. Furthermore, clemastine does not improve visual evoked potential latency following demyelinating injury when administered to a transgenic animal incapable of forming new myelin. Therefore, using the capacity for therapeutic enhancement and biological loss of function we demonstrate conclusively that visual evoked potential measures myelin status and is thereby a validated tool for preclinical verification of remyelination.

Nontrivial Topological States in BaSn5 Superconductor Probed by de Haas–van Alphen Quantum Oscillations

We report the nontrivial topological states in an intrinsic type-II superconductor BaSn 5 (T c ∼ 4.4 K) probed by measuring the magnetization, specific heat, de Haas–van Alphen (dHvA) effect, and by performing first-principles calculations. The first-principles calculations reveal a topological nodal ring structure centered at the H point in the k z = π plane of the Brillouin zone, which could be gapped by spin-orbit coupling (SOC), yielding relatively small gaps below and above the Fermi level of about 0.04 eV and 0.14 eV, respectively. The SOC also results in a pair of Dirac points along the Γ–A direction, located at ∼ 0.2 eV above the Fermi level. The analysis of the dHvA quantum oscillations supports the calculations by revealing a nontrivial Berry phase originating from the hole and electron pockets related to the bands forming the Dirac cones. Thus, our study provides an excellent avenue for investigating the interplay between superconductivity and nontrivial topological states.

Observation of dimension-crossover of a tunable 1D Dirac fermion in topological semimetal NbSixTe2

Condensed matter systems in low dimensions exhibit emergent physics that does not exist in three dimensions. When electrons are confined to one dimension (1D), some significant electronic states appear, such as charge density wave, spin-charge separations, and Su-Schrieffer-Heeger (SSH) topological state. However, a clear understanding of how the 1D electronic properties connects with topology is currently lacking. Here we systematically investigated the characteristic 1D Dirac fermion electronic structure originated from the metallic NbTe2 chains on the surface of the composition-tunable layered compound NbSixTe2 (x = 0.40 and 0.43) using angle-resolved photoemission spectroscopy. We found the Dirac fermion forms a Dirac nodal line structure protected by the combined widetilde {M_y} and time-reversal symmetry T and proves the NbSixTe2 system as a topological semimetal, in consistent with the ab-initio calculations. As x decreases, the interaction between adjacent NbTe2 chains increases and Dirac fermion goes through a dimension-crossover from 1D to 2D, as evidenced by the variation of its Fermi surface and Fermi velocity across the Brillouin zone in consistence with a Dirac SSH model. Our findings demonstrate a tunable 1D Dirac electron system, which offers a versatile platform for the exploration of intriguing 1D physics and device applications.

Embedded topological semimetals

Topological semimetals, such as Dirac, Weyl, or line-node semimetals, are gapless states of matter characterized by their nodal band structures and surface states. In this work, we consider layered (topologically trivial) insulating systems in $D$ dimensions that are composed of coupled multi-layers of $d$-dimensional topological semimetals. Despite being nominal bulk insulators, we show that crystal defects having co-dimension $(D-d)$ can harbor robust lower dimensional topological semimetals embedded in a trivial insulating background. As an example we show that defect-bound topological semimetals can be localized on stacking faults and partial dislocations. Finally, we propose how an embedded topological Dirac semimetal can be identified in experiment by introducing a magnetic field and resolving the relativistic massless Dirac Landau level spectrum at low energies in an otherwise gapped system.

Complete classification of band nodal structures and massless excitations

Nodal structures (NSrs) where energy bands meet to be degenerate in the Brillouin zone (BZ) in the form of point, line or surface, received immense research interest in the past decade. However, the nearly NSrs with negligible gaps, can also own many exotic quantum responses and nontrivial topological properties and deserve a systematic investigation. Here, we provide a complete list of all symmetry-diagonalizable strictly and nearly NSrs in the 1651 magnetic space groups (MSGs) and 528 magnetic layer groups (MLGs) in both spinful and spinless settings. We first apply compatibility relations (CRs) which encode how bands split from a band node (BN) (located at a symmetric point of BZ), to obtain all NSrs (emanating from the BN). The NSrs by CRs are definitely strict and are exhaustively enumerated based on all irreducible representations of the little groups for all BNs. We then construct $k\cdot p$ models around BNs and prove that there is a cutoff $k\cdot p$ order (6 at most) for any BN which is sufficient to predict the corresponding strictly NSrs and including higher-order $k\cdot p$ terms cannot gap the NSrs. We provide all $k\cdot p$ models up to the cutoff orders around all the BNs, and comprehensively explore all the nearly NSrs by lowering the $k\cdot p$ order. Our results reveal that the same as BNs, the NSrs, especially the nearly NSrs, are also ubiquitous. For example, while strictly nodal surface can only exist in some nonsymmorphic MSGs, nearly nodal surface can occur even in many low symmetric MSGs. Moreover, we also find that for some BNs, the method of $k\cdot p$ modeling could give more strictly NSrs than CRs. With our complete list, one can conveniently obtain all possible NSrs for any two/three-dimensional and nonmagnetic/magnetic material, and given a target NSr, one can also design/search for materials realizations based on the MSGs/MLGs.

Evaluating tectonic dislocations formation under the action of stresses at the Upper Kama potassium salt deposits

Introduction. The studies of the tectonic structure, dynamic behavior and prediction of the areas of the most probable manifestation of hazardous dynamic events at the Upper Kama potassium salt deposits (VKMKS) revealed that active faults, nodal structures, fracture zones and individual fractures in the oversalt, salt and subsalt rocks exercise a decisive influence on the violation of the steady state of geological structure. The regional stress field and a large number of local factors caused by folding, basement tectonics (catagenetic and supergene leaching), exogenous (weathering and unloading) and endogenous (halokinesis) processes in the oversalt strata, the growth of dome structures, etc. cause tectonic dislocations in the VKMKS. Cracks and fissure zones have currently been incidentally mapped and quantitatively studied mainly in mine workings in the productive part of the deposit, to a lesser extent in the oversalt rock, and scarcely in subsalt deposits. A detailed high-precision gravity prospecting along with other geophysical methods is currently the only effective method for tectonic dislocations mapping in the rock mass of the VKMKS. Methods for the widespread and systematic mapping of tectonic dislocations both in plan and in section within the VKMKS have not been developed yet. However, the evaluation of kinematic tectonic dislocations development in bulk can be obtained to some extent by analyzing the qualitative and quantitative characteristics of the natural stress field. It is due to the fact that dislocations are formed only when the acting stress exceeds the limit of the corresponding longterm strength of rocks forming the object under study. Methods of research. Tectonic dislocations of various kinematic types are formed under the action of stresses. Kinematic dislocations depend on the relationships between the stress principal values. Therefore, to solve the problem of kinematic type in the Solikamsk depression (SD) and VKMKS, the data of natural stress field components measurement in Ural mine workings were analyzed, the regularities of its behavior in plan and depth were determined, which served as the basis for two mathematical models, regional and local. Research results. Mathematical modeling was carried out, giving a quantification of stress components behavior regularities with the depth for the tectonic and physical-geological conditions of SD and VKMKS. Conclusions. The data on the change in stress components, obtained from mathematical modeling for two models of the geological environment, made it possible to predict the regularities in formation of tectonic dislocations of various kinematic types at different depths in SD and VKMKS at the regional and detailed scale levels.

Loss of \u03b24-spectrin impairs Nav channel clustering at the heminode and temporal fidelity of presynaptic spikes in developing auditory brain

Beta-4 (β4)-spectrin, encoded by the gene Sptbn4, is a cytoskeleton protein found at nodes and the axon initial segments (AIS). Sptbn4 mutations are associated with myopathy, neuropathy, and auditory deficits in humans. Related to auditory dysfunction, however, the expression and roles of β4-spectrin at axon segments along the myelinated axon in the developing auditory brain are not well explored. We found during postnatal development, β4-spectrin is critical for voltage-gated sodium channel (Nav) clustering at the heminode along the nerve terminal, but not for the formation of nodal and AIS structures in the auditory brainstem. Presynaptic terminal recordings in Sptbn4geo mice, β4-spectrin null mice, showed an elevated threshold of action potential and increased failures during action potential train at high-frequency. Sptbn4geo mice exhibited a slower central conduction and showed no startle responses, but had normal cochlear function. Taken together, the lack of β4-spectrin impairs Nav clustering at the heminode along the nerve terminal and the temporal fidelity and reliability of presynaptic spikes, leading to central auditory processing deficits during postnatal development.

Gapless excitations inside the fully gapped kagome superconductors AV3Sb5

The superconducting gap structures in the transition-metal-based kagome metal AV$_3$Sb$_5$ (A=K,Rb,Cs), the first family of quasi-two-dimensional kagome superconductors, remain elusive as there is strong experimental evidence for both nodal and nodaless gap structures. Here we show that the dichotomy can be resolved because of the coexistence of time-reversal symmetry breaking with a conventional fully gapped superconductivity. The symmetry protects the edge states which arise on the domains of the lattice symmetry breaking order to remain gapless in proximity to a conventional pairing. We demonstrate this result in a four-band tight-binding model using the V $d_{X^2-Y^2}$-like and the in-plane Sb $p_z$-like Wannier functions that can faithfully capture the main feature of the materials near the Fermi level.

Exact crystalline solution for a one-dimensional few-boson system with point interaction

We study the exact solutions for a one-dimensional system of N = 2; 3 spinless point bosons for zero boundary conditions. In this case, we are based on M Gaudin’s formulae obtained with the help of Bethe ansatz. We find the density profile ρ(x) and the nodal structure of a wave function for a set of the lowest states of the system for different values of the coupling constant γ ⩾ 0. The analysis shows that the ideal crystal corresponds to the quantum numbers (from Gaudin’s equations) n 1 = ⋯ = n N = N and to the coupling constant γ ≲ 1. We also find that the ground state (GS) of the system (n 1 = ⋯ = n N = 1) corresponds to a liquid for any γ and any N ≫ 1. In this case, the wave function of the GS is nodeless, and the wave function of the ideal crystal has nodes.

Inherited topological superconductivity in two-dimensional Dirac semimetals

Under what conditions does a superconductor inherit topologically protected nodes from its parent normal state? In the context of inter-Fermi-surface pairing in three-dimensional Weyl semimetals with broken time-reversal symmetry, the pairing order parameter is classified by monopole harmonics and is necessarily nodal [Li and Haldane, Phys. Rev. Lett. 120, 067003 (2018)]. Here, we show that a similar conclusion could also be drawn for 2D Dirac semimetals, although the conditions for the existence of nodes are more complex, depending on the pairing matrix structure in the valley and sublattice space. We analytically and numerically analyze the Bogoliubov-de Gennes quasiparticle spectra for Dirac systems based on the monolayer as well as twisted bilayer graphene. We find that in the cases of intravalley intrasublattice and intervalley intersublattice pairings, the point nodes in the BdG spectra (which are inherited from the Dirac cone in the normal state) are protected by a 1D winding number. The nodal structure of the superconductivity is confirmed numerically using tight-binding models of monolayer and twisted bilayer graphene. Notably, the BdG spectrum is nodal even with a momentum-independent ``bare'' pairing, which, however, acquires a momentum dependence and point nodes upon projection to the Bloch states on the topologically nontrivial Fermi surface, similar in spirit to the Li-Haldane monopole superconductor and the Fu-Kane proximity-induced superconductor on the surface of a topological insulator.