Topological Critical Point Research Articles

Ground-state phase diagram and universality of sequential topological valence-bond-solid quantum transitions in a mixed tetramer chain

The ground-state ordering of a quantum mixed-spin Heisenberg tetramer chain composed of an alternate sequence of s = 1 and S=3/2 dimers is studied in detail as a function of two considered exchange interactions ascribed to similar and dissimilar spin pairs. At zero magnetic field, the ferrimagnetic mixed spin-(1, 1, 3/2, 3/2) Heisenberg tetramer chain displays, depending on a mutual interplay between two considered exchange interactions, three distinct gapped valence-bond-solid phases separated by gap-closing quantum critical points. Using density-matrix renormalization group calculations we construct the full ground-state phase diagram as a function of the interaction ratio and magnetic field, which exhibits besides three gapped valence-bond-solid phases special Kosterlitz–Thouless and topological quantum critical points. A tangential finite-size scaling analysis is employed to obtain precise estimates of the zero-field valence-bond-solid transitions and unveil their common logarithmic correction to a power-law scaling of the correlation length.

Anomalous Hall effect and Fermi surface reconstruction in topological antiferromagnet candidate GdAuPb

The combination of topology and magnetism has demonstrated great potential in the search of emergent quantum matters. In this study, we report the synthesis, magnetic, and electrical properties of GdAuPb, a rare-earth-based half-Heusler topological antiferromagnet candidate. Magnetization and specific heat studies reveal highly frustrated antiferromagnetic ordering of Gd at TN = 11.5 K. Interestingly, this material possesses a large, unsaturated magnetoresistance up to 800% below TN and anomalous Hall conductivity as large as 750 Ω−1cm−1 in the antiferromagnetic state. Moreover, the electric transports including the SdH quantum oscillation patterns all exhibit a sudden change around 9 T, indicating a field-driven quantum transition related to the Fermi surface reconstruction. These results suggest that GdAuPb is close to a topological critical point, which can be easily tuned via external parameters. Our study demonstrates a strong interplay between band topology and magnetism in GdAuPb and offers clues for material designs for topological antiferromagnets.

Large anomalous Hall effect and negative magnetoresistance in half-topological semimetals

Proposed mechanisms for large intrinsic anomalous Hall effect (AHE) in magnetic topological semimetals include diverging Berry curvatures of Weyl nodes, anticrossing nodal rings or points of non-trivial bands. Here we demonstrate that a half-topological semimetal (HTS) state near a topological critical point can provide an alternative mechanism for a large AHE via systematic studies on an antiferromagnetic (AFM) half-Heusler compound TbPdBi. We not only observe a large AHE with tanΘH ≈ 2 in its field-driven ferromagnetic (FM) phase, but also find a distinct Hall resistivity peak in its canted AFM phase. Moreover, we observe a large negative magnetoresistance with a value of ~98%. Our in-depth theoretical modelling indicates that these exotic transport properties originate from the HTS state which exhibits Berry curvature cancellation between the trivial spin-up and nontrivial spin-down bands. Our study offers alternative strategies for improved materials design for spintronics and other applications.

Discrete global symmetries and dynamics of emergent fermions

Global symmetries that define the number of low-energy degrees of freedom have profound consequences on universal properties near topological quantum critical points and in other gapless or nearly gapless states of emergent fermions. We take a ${Z}_{2}$ global symmetry (such as time-reversal) as an example to study its effect on thermodynamic and transport properties. Although the thermal entropy density of ${Z}_{2}$ symmetric systems is simply twice that of their counterparts without any global symmetries or the ${Z}_{1}$ class, the temperature dependence of thermal conductivity $\ensuremath{\kappa}$ is distinctly and drastically different for different symmetries. For systems with dynamic exponent $z=1$, in the ${Z}_{2}$ symmetric class, we have $\ensuremath{\kappa}\ensuremath{\propto}{T}^{\ensuremath{-}(d\ensuremath{-}1)}$ in the quantum critical regime near weakly interacting fixed points, while for systems with no global symmetries (i.e., the ${Z}_{1}$ class), we have $\ensuremath{\kappa}\ensuremath{\propto}{T}^{\ensuremath{-}(d+3)}$, with $d$ being the spatial dimension. Only near strong-coupling fixed points, both cases with or without ${Z}_{2}$ global symmetries follow the same scaling function, $\ensuremath{\kappa}\ensuremath{\propto}{T}^{d\ensuremath{-}1}$. These distinct scalings of thermal conductivity can also appear in gapless surface Majorana states.

Electron Density Analysis of Metal–Metal Bonding in a Ni4 Cluster Featuring Ferromagnetic Exchange

We present a combined experimental and theoretical study of the nature of the proposed metal-metal bonding in the tetranuclear cluster Ni4(NPtBu3)4, which features four nickel(I) centers engaged in strong ferromagnetic coupling. High-resolution single-crystal synchrotron X-ray diffraction data collected at 25 K provide an accurate geometrical structure and a multipole model electron density description. Topological analysis of the electron density in the Ni4N4 core using the quantum theory of atoms in molecules clearly identifies the bonding as an eight-membered ring of type [Ni-N-]4 without direct Ni-Ni bonding, and this result is generally corroborated by an analysis of the energy density distribution. In contrast, the calculated bond delocalization index of ∼0.6 between neighboring Ni atoms is larger than what has been found for other bridged metal-metal bonds and implies direct Ni-Ni bonding. Similar support for the presence of direct Ni-Ni bonding is found in the interacting quantum atom approach, an energy decomposition scheme, which suggests the presence of stabilizing Ni-Ni bonding interactions with an exchange-correlation energy contribution approximately 50% of that of the Ni-N interactions. Altogether, while the direct interactions between neighboring Ni centers are too weak and sterically constrained to bear the signature of a topological bond critical point, other continuous measures clearly indicate significant Ni-Ni bonding. These metal-metal bonding interactions likely mediate direct ferromagnetic exchange, giving rise to the high-spin ground state of the molecule.

Investigation of the interionic interactions and spectroscopic features of 1-Octyl-3-methylimidazolium chloride, tetrafluoroborate, and hexafluorophosphate ionic liquids: An experimental survey and DFT modeling

This study presents the spectroscopic and electronic properties of some imidazole-based ionic liquids (ILs) consisting of 1-Octyl-3-methylimidazolium cation and chloride, tetrafluoroborate, and hexafluorophosphate anions from experimental and theoretical perspectives. The ground state structural and vibrational characteristics of the ionic liquids have been achieved through Density Functional Theory (DFT) calculations at the Becke's and the Lee–Yang–Parr (B3LYP) and 6–311++G(d,p) level of theory in Gaussian 16. The electronic and magnetic features of the ILs have been examined by using electronic absorption spectra and Nuclear Magnetic Resonance spectroscopy (NMR) techniques along with the calculations from Time-Dependent Density Functional Theory (TD-DFT) and using Gauge-Including Atomic Orbital (GIAO) method.The intra- and interionic noncovalent interactions in the ionic liquids have been revealed via the electron density analysis based on the Atoms in Molecules (AIM) approach, and decomposed as hydrogen bonding, van der Waals interactions, and steric effects via Reduced Density Gradient (RDG) analysis. To gain insight into the possible effects of anion-cation interaction on the physicochemical properties of ionic liquids, interionic interactions, reactivity properties, topological critical points, and electrostatic potential surfaces were obtained. These interactional characteristics were interpreted in terms of both the anion dependency and interaction type. Notably, the results of this study were evaluated together with the results obtained from our previous study on ILs consisting of the same anions with the 1-Hexyl-3-methylimidazolium cation to achieve the effects of the extension in the chain length of the cation in the presence of the same anion on the spectroscopic and electronic properties of ionic liquids.

Topological Quantum Critical Points in the Extended Bose-Hubbard Model.

The combination of topology and quantum criticality can give rise to an exotic mix of counterintuitive effects. Here, we show that unexpected topological properties take place in a paradigmatic strongly correlated Hamiltonian: the 1D extended Bose-Hubbard model. In particular, we reveal the presence of two distinct topological quantum critical points with localized edge states and gapless bulk excitations. Our results show that the topological critical points separate two phases, one topologically protected and the other topologically trivial, both characterized by a long-range ordered string correlation function. The long-range order persists also at the topological critical points and explains the presence of localized edge states protected by a finite charge gap. Finally, we introduce a superresolution quantum gas microscopy scheme for dipolar dysprosium atoms, which provides a reliable route towards the experimental study of topological quantum critical points.

Topological quantum critical points in strong coupling limits: Global symmetries and strongly interacting Majorana fermions

In this paper, we discuss strong coupling limits of topological quantum critical points (TQCPs) where quantum phase transitions between two topological distinct superconducting states take place. We illustrate that while superconducting phases on both sides of TQCPs spontaneously break the same symmetries, universality classes of critical states can be identified only when global symmetries in topological states are further specified. In dimensions $d=2\phantom{\rule{4.pt}{0ex}}\text{and}\phantom{\rule{4.pt}{0ex}}3$, we find that continuous $(d+1)\mathrm{th}$-order transitions at weakly interacting TQCPs that were pointed out previously in the presence of the emergent Lorentz symmetry can be terminated by strongly interacting fixed points of Majorana fields. For $2d$ time reversal symmetry breaking TQCPs, termination points are supersymmetric with $\mathcal{N}=4{N}_{f}=1$ (where ${N}_{f}$ is the number of four-component Dirac fermions and $\mathcal{N}$ is the number of two-component real fermions) beyond which transitions are discontinuous first-order ones. For $2d$ time reversal symmetric TQCPs without other global symmetries, termination points of $(d+1)\mathrm{th}$-order continuous transition lines are generically conformal invariant without supersymmetry. Beyond these strong coupling fixed points, there are first-order discontinuous transitions as far as the protecting symmetry is not spontaneously broken but no direct transitions if the protecting symmetry is spontaneously broken in the presence of strong interactions. In this case, termination points can become supersymmetric with $\mathcal{N}=4{N}_{f}=2$ only when interacting Majorana fermions further display an emergent global $\text{U}(1)$ symmetry. In $3d$, strong coupling termination points can be further effectively represented by new emergent gapless real bosons weakly coupled with free gapless Majorana fermions. However, in $1d$, time reversal symmetric $(d+1)\mathrm{th}$ continuous transition lines of TQCPs are terminated by simple free Majorana fermion fixed points.

On the Characteristics of the Super-Critical Wake behind a Circular Cylinder

The flow topology of the wake behind a circular cylinder at the super-critical Reynolds number of Re=7.2×105 is investigated by means of large eddy simulations. In spite of the many research works on circular cylinders, there are no studies concerning the main characteristics and topology of the near wake in the super-critical regime. Thus, the present work attempts to fill the gap in the literature and contribute to the analysis of both the unsteady wake and the turbulent statistics of the flow. It is found that although the wake is symmetric and preserves similar traits to those observed in the sub-critical regime, such as the typical two-lobed configuration in the vortex formation zone, important differences are also observed. Owing to the delayed separation of the flow and the transition to turbulence in the attached boundary layer, Reynolds stresses peak in the detached shear layers close to the separation point. The unsteady mean flow is also investigated, and topological critical points are identified in the vortex formation zone and the near wake. Finally, time-frequency analysis is performed by means of wavelets. The study shows that in addition to the vortex shedding frequency, the inception of instabilities that trigger transition to turbulence occurs intermittently in the attached boundary layer and is registered as a phenomenon of variable intensity in time.

Nonlinear optical behavior of non‐centrosymmetric biferrocenyl Schiff‐base derivatives and their DNA binding potential supported by DFT and electrochemical investigations

AbstractTwo new non‐centrosymmetric biferrocenyl Schiff bases, that is, N‐(ferrocenylmethylene)‐4‐(4‐(ferrocenylmethyleneamino)phenoxy)benzenamine (FeL1) and 4,4′‐([1,1′‐biferrocenyl]‐4,4′‐diylbis(methylene)bis(N‐benzylideneaniline) (FeL2), have been synthesized and studied by density functional theory (DFT) to understand their nonlinear optical (NLO) behavior. The synthesized compounds were characterized by FTIR, NMR, and UV–visible spectroscopic techniques. DFT studies were performed to obtain the polarizability and first‐order hyperpolarizability parameters useful in determining the NLO response. Results indicate that the substituted biferrocenyl Schiff bases show a substantial increase in first‐order hyperpolarizability (44 times greater than the reference urea) compared with unsubstituted ferrocene. The enhanced NLO behavior follows the trend FeL2 > FeL1 > urea. Bader's atoms in molecules (AIM) theory has been employed to obtain topological parameters and critical points to evaluate the nature and strength of different types of intramolecular interactions. Charge delocalization in the complexes was investigated through natural bond order (NBO) analysis. It was observed that intramolecular charge transfer (ICT) is responsible for the optical nonlinearity of the biferrocenyl Schiff bases, with hydrogen bonding playing a prominent role in the bonding networks leading to increased hyperpolarizability. Furthermore, molecular electrostatic potential (MEP) surfaces of the molecular systems have also been analyzed. From an application viewpoint, the interaction of the biferrocenyl derivatives with fish‐sperm DNA was studied through spectrophotometric and electrochemical measurements. Results indicate major groove binding with DNA, which is also predicted by molecular docking studies.

Effect of divider wall-to-end wall distance on the vortical structures and heat transfer characteristics of two-pass channel using topological analysis

PurposeThis study aims to explore the 3 D separated flow fields and heat transfer characteristics at the end wall of a serpentine channel with various turn clearances using topological analysis and critical points principles of three-dimensional vortex flow.Design/methodology/approachThis aims to explore the 3 D separated flow fields and heat transfer characteristics at the end wall of a serpentine channel with various turn clearances using topological analysis as well as critical points principles of three-dimensional vortex flow.FindingsThe endwall heat transfer in the narrow spacing passage is significantly stronger than that in a wide spacing channel. As the gap clearance is kept at 0.87 times of the hydraulic diameter, the endwall heat transfer and thermal performance can be accordingly enhanced with low pressure drops, which is because a relatively strong concentrated impingement flow for the medium gap clearance helps to restrain the downstream fluid flow and enhance the shear effect of the secondary flow.Practical implicationsThe numerical results can be applied in designing sharp turn of serpentine channel in heat exchangers, heat sinks, piping system, solar receiver and gas turbine blades.Originality/valueThe evolution mechanism of the vortices in the turning region under different gap clearance was analyzed, and thermal enhancement characteristics were predicted innovatively using topological analysis method.

Prediction of tunable spin-orbit gapped materials for dark matter detection

New ideas for low-mass dark matter direct detection suggest that narrow band gap materials, such as Dirac semiconductors, are sensitive to the absorption of meV dark matter or the scattering of keV dark matter. Here we propose spin-orbit semiconductors - materials whose band gap arises due to spin-orbit coupling - as low-mass dark matter targets owing to their ~10 meV band gaps. We present three material families that are predicted to be spin-orbit semiconductors using Density Functional Theory (DFT), assess their electronic and topological features, and evaluate their use as low-mass dark matter targets. In particular, we find that that the tin pnictide compounds are especially suitable having a tunable range of meV-scale band gaps with anisotropic Fermi velocities allowing directional detection. Finally, we address the pitfalls in the DFT methods that must be considered in the ab initio prediction of narrow-gapped materials, including those close to the topological critical point.

Detecting topological quantum phase transitions via the c-function

We propose the c-function as a new and accurate probe to detect the location of topological quantum critical points. As a direct application, we consider a holographic model which exhibits a topological quantum phase transition between a topologically trivial insulating phase and a gapless Weyl semimetal. The quantum critical point displays a strong Lifshitz-like anisotropy in the spatial directions and the quantum phase transition does not follow the standard Landau paradigm. The c-function robustly shows a global feature at the quantum criticality and distinguishes with great accuracy the two separate zero temperature phases. Taking into account the relation of the c-function with the entanglement entropy, we conjecture that our proposal is a general feature of quantum phase transitions and that is applicable beyond the holographic framework.

Understanding Reactivity and Assembly of Dichalcogenides: Structural, Electrostatic Potential, and Topological Analyses of 3H-1,2-Benzodithiol-3-one and Selenium Analogs

Molecular assembly and reactivity have been investigated with a series of 3H-1,2-benzodithiol-3-(thi)one derivatives and their (mixed) selenated analogs. Electrostatic potential calculations on monomers show three σ-hole regions around the dichalcogenide Ch-Ch bond (Ch = S, Se), one side-on and two along the bonding direction. The topological analysis of the electron density ρ(r) points to the weak nature of the Ch-Ch bond. σ-Hole and lone-pair regions are described in terms of charge depletion (CD) and charge concentration (CC) sites found in the valence shell of chalcogen atoms. Whereas CD and CC sites are characterized by the topological critical points of L(r) = -2ρ(r), their electrophilic and nucleophilic powers are measured by the corresponding L/ρ magnitudes. In crystal structures, each chalcogen bond (ChB) involves a σ-hole region and shows a CD⋯CC interaction that aligns with the internuclear direction of the atoms the CD and CC sites belong. The alignment holds simultaneously for all of the ChB interactions in each crystal structure, indicating that CD⋯CC interactions drive molecular orientation in molecular assembly. Strength of ChB is measured in terms of the topological properties of ρ(r), whereas the intensity of the electrophilic⋯nucleophilic interaction is monitored by [(L/ρ)CC - (L/ρ)CD]/dCC⋯CD2. The σ-hole in side-on conformation forms the strongest ChB interactions in molecular assembly. Reactivity of molecules against nucleophilic attack has been investigated along each of the three σ-hole regions by using fluoride as a probe. Adducts formed along the Ch-Ch bonding direction are energetically more favorable than in side-on conformation. At optimized geometries, the F⋯Ch bond (Ch = S, Se) exhibits a partial covalent character, while it weakens concomitantly the Ch⋯Ch bond that also becomes of partial covalent character. In the reactivity process, the significant reorientation of the plane containing the chalcogen lone pairs, along with the opening, shrinking, and splitting of reactivity surfaces 2ρ(r) = 0, is the signature of the charge redistribution that involves the nucleophilic attack. © 2020 American Chemical Society.

Multiplicity results for double phase problems in RN

We consider a double phase problem in RN with a q−1-superlinear subcritical Carathéodory reaction term, which does not satisfy the Ambrosetti–Rabinowitz condition. Using variational methods based on the topological degree and critical point theory together with the Nehari manifold method and deformation lemma, we find three nontrivial solutions: among them, the first one is the positive ground state solution, the second one is the negative ground state solution, and the third one is the least energy sign-changing solution, which changes sign only once. We also discuss the existence of infinitely many solutions for even energy functional and that of radial solutions.

Localized nodal solutions of higher topological type for nonlinear Schrödinger–Poisson system

In this paper, we focus our attention on following Schrödinger–Poisson system: −ε2Δu+V(x)u+λψu=|u|p−2u,x∈R3,−ε2Δψ=u2,u∈H1(R3).where 4<p<6 and ε,λ>0 are small positive parameters. Under a local condition imposed on the potential V, we study above system and obtain an infinite sequence of localized sign-changing solutions by applying the symmetric mountain pass theorem. Precisely, these solutions are constructed as higher topological type critical points of the energy functional and concentrated at a local minimum set of the potential V. Our method follows the same spirit of Chen and Wang’s method (Chen and Wang, 2017) which does not need any non-degeneracy condition of the limiting equations, but we cannot use it directly due to the presence of nonlocal term ψ(x)=14π∫R3u2(y)|x−y|dy. We employ some new analytical skills to overcome the obstacles caused by the nonlocal term, our results improve and extend some related ones in the literature.

Nonsmooth critical point theory and applications to the spectral graph theory

Existing critical point theories including metric and topological critical point theories are difficult to be applied directly to some concrete problems in particular polyhedral settings, because the notions of critical sets could be either very vague or too large. To overcome these difficulties, we develop the critical point theory for nonsmooth but Lipschitzian functions defined on convex polyhedrons. This yields natural extensions of classical results in the critical point theory, such as the Liusternik-Schnirelmann multiplicity theorem. More importantly, eigenvectors for some eigenvalue problems involving graph 1-Laplacian coincide with critical points of the corresponding functions on polytopes, which indicates that the critical point theory proposed in the present paper can be applied to study the nonlinear spectral graph theory.

Odd-frequency pairing and proximity effect in Kitaev chain systems including a topological critical point

In this paper, we investigate the relation between odd-frequency pairing and proximity effect in non-uniform Kitaev chain systems with a particular interest in the topological critical point. First, we correlate the odd-frequency pairing and Majorana fermion in a semi-infinite Kitaev chain, where we find that the spatial dependence of the odd-frequency pair amplitude coincides with that of the local density of states at low frequencies. Second, we demonstrate that, contrary to the standard view, the odd-frequency pair amplitude spreads into the bulk of a semi-infinite Kitaev chain at the topological critical point. Finally, we show that odd-frequency Cooper pairs cause the proximity effect in a normal metal/diffusive normal metal/ Kitaev chain junction even at the topological critical point. Our results hold relevance to the investigation of odd-frequency pairing and topological superconductivity in more complicated systems that involve Rashba nanowire with magnetic fields.

Bound states for logarithmic Schrödinger equations with potentials unbounded below

We study the existence and concentration behavior of the bound states for the following logarithmic Schr\"odinger equation \begin{equation*} \begin{cases} -\varepsilon^2\Delta v+V(x)v=v\log v^2 \ \ &\text {in}\ \ \mathbb R^N,\\ v(x)\to 0 \ \ &\text {as}\ \ |x|\to\infty, \end{cases} \end{equation*} where $N\geq 1$, $\varepsilon>0$ is a small parameter, and $V$ may be unbounded below at infinity with a speed of at most quadratic strength. We show that around various types of local topological critical points of the potential function, positive bound state solutions exist and concentrate as $\varepsilon\to0$.

A special triple point in non-centrosymmetric materials Zn3In2Se6 and In2Se3

We predict that the non-centrosymmetric materials Zn3In2Se6 and In2Se3 are the symmetry protected topological critical triple point metals based on first principles calculation. The dispersion along the Γ-Z line almost vanishes because of the particular crystal structure, and the strain along the c direction maybe drives accidental Dirac point to triple point. An effective theory is developed to describe accidental Dirac points and triple points, by which we calculate the surface states. These materials provide us a new platform to discuss the relation between the triple points and Dirac points.