Nodal Structure Research Articles

Crh receptor priming in the bed nucleus of the stria terminalis (BNST) induces tph2 gene expression in the dorsomedial dorsal raphe nucleus and chronic anxiety

The bed nucleus of the stria terminalis (BNST) is a nodal structure in neural circuits controlling anxiety-related defensive behavioral responses. It contains neurons expressing the stress- and anxiety-related neuropeptide corticotropin-releasing hormone (Crh) as well as Crh receptors. Repeated daily subthreshold activation of Crh receptors in the BNST is known to induce a chronic anxiety-like state, but how this affects neurotransmitter-relevant gene expression in target regions of the BNST is still unclear. Since the BNST projects heavily to the dorsal raphe nucleus (DR), the main source of brain serotonin, we here tested the hypothesis that such repeated, anxiety-inducing activation of Crh receptors in the BNST alters the expression of serotonergic genes in the DR, including tph2, the gene encoding the rate-limiting enzyme for brain serotonin synthesis, and slc6a4, the gene encoding the serotonin transporter (SERT). For 5 days, adult male Wistar rats received daily, bilateral, intra-BNST microinjections of vehicle (1% bovine serum albumin in 0.9% saline, n = 11) or behaviorally subthreshold doses of urocortin 1 (Ucn1, n = 11), a potent Crh receptor agonist. Priming with Ucn1 increased tph2 mRNA expression selectively within the anxiety-related dorsal part of the DR (DRD) and decreased social interaction (SI) time, a measure of anxiety-related defensive behavioral responses in rodents. Decreased social interaction was strongly correlated with increased tph2 mRNA expression in the DRD. Together with previous studies, our data are consistent with the hypothesis that Crh-mediated control of the BNST/DRD-serotonergic system plays a key role in the development of chronic anxiety states, possibly also contributing to stress-induced relapses in drug abuse and addiction behavior.

Courant-sharp Robin eigenvalues for the square: the case with small Robin parameter

This article is the continuation of our first work on the determination of the cases where there is equality in Courant’s Nodal Domain theorem in the case of a Robin boundary condition (with Robin parameter h). For the square, our first paper focused on the case where h is large and extended results that were obtained by Pleijel, Berard–Helffer, for the problem with a Dirichlet boundary condition (which corresponds to $$h=+\infty $$). There, we also obtained some general results about the behaviour of the nodal structure (for planar domains) under a small deformation of h, where h is positive and not close to 0. In this second paper, we extend results that were obtained by Helffer–Persson Sundqvist for the Neumann problem (which corresponds to $$h=0$$) to the case where $$ h>0$$ is small.

Hyperbolic nodal band structures and knot invariants

We extend the list of known band structure topologies to include a large family of hyperbolic nodal links and knots, occurring both in conventional Hermitian systems where their stability relies on discrete symmetries, and in the dissipative non-Hermitian realm where the knotted nodal lines are generic and thus stable towards any small perturbation. We show that these nodal structures, taking the forms of Turk’s head knots, appear in both continuum- and lattice models with relatively short-ranged hopping that is within experimental reach. To determine the topology of the nodal structures, we devise an efficient algorithm for computing the Alexander polynomial, linking numbers and higher order Milnor invariants based on an approximate and well controlled parameterisation of the knot.

Symmetry of superconducting pairing in non-pseudospin electron bands

We develop the symmetry classification of superconducting gap functions in electron bands that do not transform under the crystal point group operations like the pure spin-1/2 states. The Bloch state bases in twofold degenerate bands with spin-orbit coupling are defined across the Brillouin zone in the way which satisfies the symmetry and continuity requirements. These bases are used to construct general multiband pairing Hamiltonians in centrosymmetric crystals. Focusing on single-band pairing, four exceptional cases are identified in which the triplet gap function does not transform under the point group operations as a pseudovector, with a significant impact on the nodal structure.

Modeling of atomistic scale shear failure of Ag/MgO interface with misfit dislocation network

Metal/ceramic interfaces have broad applications and misfit dislocation network (MDN) is a prominent feature of the equilibrium metal/ceramic interfaces. As one main failure mode, interface shear failure is strongly affected by the motion of MDN. In this work, we investigate the equilibrium interface structure and shear failure of Ag/MgO interface via atomistic simulation method. Periodically distributed in-plane strain field caused by MDN and severe strain concentration at dislocation node regions are found by strain analysis. During interface shearing, these dislocation nodes act as strong pinning points to the gliding motion of MDN, which leads to bending of dislocation lines. Besides, energy analysis shows the interface shear stress is largely dependent on the variation of misfit dislocation energy. To understand interface shear failure under more complex conditions, we study the effect of model thickness and shear direction further. Due to transformation of nodal structure, the shear strength of thick model eventually decreases by almost a quarter; shear failure along the direction of Burgers vector is found to be energetically favored, with the lowest interface shear strength. This work reveals the crucial role of MDN in interface shear process, and the theoretical understanding gives some hints to metal/ceramic interface design.

Solving the Trivial Crossing Problem While Preserving the Nodal Symmetry of the Wave Function.

In an adiabatic mixed quantum-classical simulation, the avoided crossing of weakly coupled eigenstates can lead to unphysical discontinuities in wave function dynamics, otherwise known as the trivial crossing problem. A standard solution to the trivial crossing problem eliminates spatial discontinuities in wave function dynamics by imposing changes to the eigenstate of the wave function. In this paper, we show that this solution has the side effect of introducing transient discontinuities in the nodal symmetry of the wave function. We present an alternative solution to the trivial crossing problem that preserves both the spatial and nodal structure of the adiabatic wave function. By considering a model of exciton dynamics on conjugated polymer systems, we show that failure to preserve wave function symmetry yields exciton dynamics that depends unphysically on polymer system size. We demonstrate that our symmetry-preserving solution to the trivial crossing problem yields more realistic dynamics and can thus improve the accuracy of simulations of larger systems that are prone to the trivial crossing problem.

Ferromagnetic nodal-line metal in monolayer h -InC

Based on first-principles calculations, we predict a new two-dimensional ferromagnetic material that exhibits exotic Fermi surface topology. We show that monolayer hexagonal indium carbide ({\em h}-InC) is thermodynamically and dynamically stable, and it energetically favors the ferromagnetic ordering of spins. The perfectly planar geometry in two dimensions, together with ferromagnetism, gives rise to a unique opportunity to encounter intriguing electronic properties, captured in the Fermi surface and band topology. We show that multiple nodal lines coexist in momentum space, accompanied by the electron and hole pockets that touch each other linearly at the nodal lines. Inclusion of spin-orbit coupling enriches the magnetic and electronic properties of {\em h}-InC. Spin-orbit coupling leads to an easy-plane type magnetocrystalline anisotropy, and the nodal lines can be tuned into topological nodal points, contingent upon the magnetization direction. Symmetry analysis and a tight-binding model are provided to explain the nodal structure of the bands. Our findings suggest {\em h}-InC as a new venue for supporting carbon-based magnetism and exotic band topology in two dimensions.

Resolving the Unpaired-Electron Orbital Distribution in a Stable Organic Radical by Kondo Resonance Mapping.

The adsorption geometry and the electronic structure of a Blatter radical derivative on a gold surface were investigated by a combination of high-resolution noncontact atomic force microscopy and scanning tunneling microscopy. While the hybridization with the substrate hinders direct access to the molecular states, we show that the unpaired-electron orbital can be probed with Ångström resolution by mapping the spatial distribution of the Kondo resonance. The Blatter derivative features a peculiar delocalization of the unpaired-electron orbital over some but not all moieties of the molecule, such that the Kondo signature can be related to the spatial fingerprint of the orbital. We observe a direct correspondence between these two quantities, including a pronounced nodal plane structure. Finally, we demonstrate that the spatial signature of the Kondo resonance also persists upon noncovalent dimerization of molecules.

Singular angular magnetoresistance in a magnetic nodal semimetal.

Transport coefficients of correlated electron systems are often useful for mapping hidden phases with distinct symmetries. Here we report a transport signature of spontaneous symmetry breaking in the magnetic Weyl semimetal cerium-aluminum-germanium (CeAlGe) system in the form of singular angular magnetoresistance (SAMR). This angular response exceeding 1000% per radian is confined along the high-symmetry axes with a full width at half maximum reaching less than 1° and is tunable via isoelectronic partial substitution of silicon for germanium. The SAMR phenomena is explained theoretically as a consequence of controllable high-resistance domain walls, arising from the breaking of magnetic point group symmetry strongly coupled to a nearly nodal electronic structure. This study indicates ingredients for engineering magnetic materials with high angular sensitivity by lattice and site symmetries.

On the Probability Density of the Nuclei in a Vibrationally Excited Molecule.

For localized and oriented vibrationally excited molecules, the qualitative features of the one-body probability density of the nuclei (one-nucleus density) are investigated. Like the familiar and widely used one-electron density that represents the probability of finding an electron at a given location in space, the one-nucleus density represents the probability of finding a nucleus at a given position in space independent of the location of the other nuclei and independent of their type. In contrast to the electrons, however, the nuclei are comparably localized. Due to this localization of the individual nuclei, the one-nucleus density provides a quantum-mechanical representation of the “chemical picture” of the molecule as an object that can largely be understood in a three-dimensional space, even though its full nuclear probability density is defined on the high-dimensional configuration space of all the nuclei. We study how the nodal structure of the wavefunctions of vibrationally excited states translates to the one-nucleus density. It is found that nodes do not necessarily lead to visible changes in the one-nucleus density: Already for relatively small molecules, only certain vibrational excitations change the one-nucleus density qualitatively compared to the ground state. It turns out that there are simple rules for predicting the shape of the one-nucleus density from the normal mode coordinates. A Python module for the computation of the one-nucleus density is provided at https://gitlab.com/axelschild/mQNMc

Streamlined Development of Analytic Fusion Capability for Health Surveillance

Streamlined Development of Analytic Fusion Capability for Health Surveillance

Electron bubbles and the structure of the orbital wave function

Stripe-like and bubble-like patterns spontaneously form in numerous physical, chemical, and biological systems when competing long-range and short-range interactions banish uniformity. Stripe-like and the related nematic morphology are also under intense scrutiny in various strongly correlated electron systems. In contrast, the electronic bubble morphology is rare. Some of the most intriguing electron bubbles develop in the two-dimensional electron gas subjected to a perpendicular magnetic field. However, in contrast to bubbles forming in classical systems such as the Turing activator-inhibitor reaction or Langmuir films, bubbles in electron gases owe their existence to elementary quantum mechanics: they are stabilized as wavefunctions of individual electrons overlap. Here we report a rich pattern of multi-electron bubble phases in a high Landau level and we conclude that this richness is due to the nodal structure of the orbital component of the electronic wavefunction.

Entropic Kullback‐Leibler type distance measures for quantum distributions

AbstractEntropic distance measures for quantum mechanical probability distributions, which are characterized by nodal structure and symmetry holes, are considered. We illustrate how the Kullback‐Leibler (KL) distance is not well defined in some instances and propose instead the use of the cumulative residual Kullback‐Leibler (CRKL) distance. The KL and CRKL measures are compared and contrasted for some representative quantum mechanical systems: The particle in an infinite well, the harmonic oscillator, and hydrogenic systems. We present cases where CRKL can be used to obtain distances whereas KL cannot be used, and also highlight examples where the KL and CRKL measures yield different behaviors and interpretations. An extension of the CRKL definition is obtained for application to harmonic oscillator systems defined over [−∞, ∞]. Distance measures for two‐variable (particle) distributions are also considered to address generalizations of the mutual information correlation measure. The use of CRKL in measuring distances between orbitals is also discussed.

Saddle solutions for the Choquard equation

We study the Choquard equation $$\begin{aligned} -\Delta u + u= (I_\alpha *|u|^p )|u|^{p-2}u \quad \text { in }\;{\mathbb {R}}^N \end{aligned}$$ where $$N\ge 2$$ , $$I_\alpha $$ is the Riesz potential of order $$\alpha \in (0, N)$$ and $$2\le p<\frac{N+\alpha }{N-2}$$ . For any given integer $$\ell \ge 2$$ , we construct a saddle type nodal solution with its $$2\ell $$ nodal domains meeting at the origin. Moreover, this equation admits nodal solutions of higher dimensional nodal structure with exactly $$2^k$$ nodal domains for each $$1\le k\le N$$ . This is a new phenomenon for the Choquard equation which is nonlocal in nature when compared with its local counterpart the nonlinear Schrodinger equation.

Phase Diagram of a Magnetic Topological Nodal Semimetal: Stable Nodal Line in an Easy-Plane Ferromagnet

We study a topological phase diagram of a ferromagnetic topological nodal semimetal. We consider a lattice model for three-dimensional topological insulators with ferromagnetic ordering. The exchange coupling between the magnetization and the electron spin leads to the nodal band structure. The topology of the nodal band structure depends on the direction of the magnetization and both the Weyl points and the nodal line emerge. We find that the nodal line structure is stable under an easy-plane magnetization in appropriate model parameters. In this case, the nodal line phase emerges as a phase boundary between two topologically distinct Weyl semimetal phases.

Large anomalous Hall and Nernst effects from nodal line symmetry breaking in Fe2MnX ( X = P, As, Sb)

A large Berry curvature in the vicinity of the Fermi energy is required in order to obtain a large anomalous Hall and Nernst effect. This Berry curvature can be induced by Weyl points and gapped nodal lines. One of the possible mechanisms takes place in systems with a symmetry group where mirror planes lead to protected nodal line structures. When these mirror symmetries are broken, e. g. via fixing a magnetization direction, a gap in the former nodal line can create Weyl points and a large Berry curvature along the gapped lines. In this work we study this effect in a minimal effective model and relate the results to the real regular Heusler compounds Fe$_2$MnX (X=P,As,Sb). These materials have three mirror planes in the non-magnetic case, leading to three nodal lines near the Fermi level. However, dependent on the orientation of the magnetization, some of the mirror planes are broken and the respective lines are gapped, creating large Berry curvature. Because the Fermi level is located in vicinity of the gapped lines, this leads to a large anomalous Hall and Nernst effect, which can be tuned to even higher values with a little bit of doping in the system.

Induced Representation Method in the Theory of Electron Structure and Superconductivity

It is shown that the application of theorems of induced representations method, namely, Frobenius reciprocity theorem, transitivity of induction theorem, and Mackey theorem on symmetrized squares, makes simplifying standard techniques in the theory of electron structure and constructing Cooper pair wavefunctions on the basis of one-electron solid-state wavefunctions possible. It is proved that the nodal structure of topological superconductors in the case of multidimensional irreducible representations is defined by additional quantum numbers. The technique is extended on projective representations in the case of nonsymmorphic space groups and examples of applications for topological superconductors UPt3 and Sr2RuO4 are considered.

Dielectric resonator method for determining gap symmetry of superconductors through anisotropic nonlinear Meissner effect.

We present a new measurement method which can be used to image the gap nodal structure of superconductors whose pairing symmetry is under debate. This technique utilizes a high quality factor microwave resonance involving the sample of interest. While supporting a circularly symmetric standing wave current pattern, the sample is perturbed by a scanned laser beam, creating a photoresponse that was previously shown to reveal the superconducting gap anisotropy. Simulation and the measurement of the photoresponse of an unpatterned Nb film show less than 8% anisotropy, as expected for a superconductor with a nearly isotropic energy gap along with expected systematic uncertainty. On the other hand, measurement of a YBa2Cu3O7-δ thin film shows a clear 4-fold symmetric image with ∼12.5% anisotropy, indicating the well-known 4-fold symmetric dx2-y2 gap nodal structure in the ab-plane. The deduced gap nodal structure can be further cross-checked by low temperature surface impedance data, which are simultaneously measured. The important advantage of the presented method over the previous spiral resonator method is that it does not require a complicated lithographic patterning process which limits one from testing various kinds of materials due to photoresponse arising from patterning defects. This advantage of the presented technique, and the ability to measure unpatterned samples such as planar thin films and single crystals, enables one to survey the pairing symmetry of a wide variety of unconventional superconductors.

Shubnikov–de Haas and de Haas–van Alphen oscillations in the topological semimetal CaAl4

We report the magneto-transport properties of CaAl$_4$ single crystals with $C2/m$ structure at low temperature. CaAl$_4$ exhibits large unsaturated magnetoresistance $\sim$3000$\%$ at 2.5 K and 14 T. The nonlinear Hall resistivity is observed, which indicates the multi-band feature. The first-principles calculations show the electron-hole compensation and the complex Fermi surface in CaAl$_4$, to which the two-band model with over-simplified carrier mobility can't completely apply. Evident quantum oscillations have been observed with B//c and B//ab configurations, from which the nontrivial Berry phase is extracted by the multi-band Lifshitz-Kosevich formula fitting. An electron-type quasi-2D Fermi surface is found by the angle-dependent Shubnikov-de Haas oscillations, de Haas-van Alphen oscillations and the first-principles calculations. The calculations also elucidate that CaAl$_4$ owns a Dirac nodal line type band structure around the $\Gamma$ point in the $Z$-$\Gamma$-$L$ plane, which is protected by the mirror symmetry as well as the space inversion and time reversal symmetries. Once the spin-orbit coupling is included, the crossed nodal line opens a negligible gap (less than 3 meV). The open-orbit topology is also found in the electron-type Fermi surfaces, which is believed to help enhance the magnetoresistance observed.

On the Nodal Structure of Nonlinear Stationary Waves on Star Graphs

We consider stationary waves on nonlinear quantum star graphs, i.e., solutions to the stationary (cubic) nonlinear Schrödinger equation on a metric star graph with Kirchhoff matching conditions at the centre. We prove the existence of solutions that vanish at the centre of the star and classify them according to the nodal structure on each edge (i.e., the number of nodal domains or nodal points that the solution has on each edge). We discuss the relevance of these solutions in more applied settings as starting points for numerical calculations of spectral curves and put our results into the wider context of nodal counting, such as the classic Sturm oscillation theorem.