Topological Vortices Research Articles

Critical Role of Sc Substitution in Modulating Ferroelectricity in Multiferroic LuFeO3.

Understanding how individual dopants or substitutional atoms interact with host lattices enables us to manipulate, control, and improve the functionality of materials. However, because of the intimate coupling among various degrees of freedom in multiferroics, the atomic-scale influence of individual foreign atoms has remained elusive. Here, we unravel the critical roles of individual Sc substitutional atoms in modulating ferroelectricity at the atomic scale of typical multiferroics, Lu1-xScxFeO3, by combining advanced microscopy and theoretical studies. Atomic variations in polar displacement of intriguing topological vortex domains stabilized by Sc substitution are directly correlated with Sc atom-mediated local chemical and electronic fluctuations. The local FeO5 trimerization magnitude and Lu/Sc-O hybridization strength are found to be significantly reinforced by Sc, clarifying the origin of the strong dependence of improper ferroelectricity on Sc content. This study could pave the way for correlating dopant-regulated atomic-scale local structures with global properties to engineer emergent functionalities of numerous chemically doped functional materials.

Effects of oscillating spacetime metric background on a complex scalar field and formation of topological vortices

We study the time evolution of a complex scalar field in the symmetry broken phase in the presence of oscillating spacetime metric background. In our (2+1)-dimensional simulations, we show that the spacetime oscillations can excite an initial field configuration, which ultimately leads to the formation of topological vortices in the system. At late times, field configuration achieves a disordered state. A detailed study of the momentum and frequency modes of the field reveals that these field excitations are driven by the phenomenon of parametric resonance. In extremely high frequency regime where frequency of spacetime oscillations is much larger than the field-mass, the formed vortices are not topological in nature. Interestingly in this regime, for a suitable choice of parameters of the simulation, we observe a persistent lattice structure of vortex-antivortex pairs. We discuss applications of our study to the dynamics of interior superfluidity of neutron stars during binary neutron star mergers, in generation of excitation in ultralight axion-like field near a strong gravitational wave source, etc.

Topological cavities in phononic plates for robust energy harvesting

Piezoelectric energy harvesting has attracted tremendous interest for designing sustainable self-powered devices/systems targeted to special environment such as wireless or wearable applications. The traditional cavity (e.g., phononic cavity mode) excitation is highly applicable in terms of sufficient power generation, nevertheless, has to endure the drawback of extremely poor robustness intrinsic to the trivial cavity modes. We propose to use phononic thin plate systems for robust energy harvesting application relying on zero-dimensional cavities confined by the Kekulé distorted topological vortices. The harvesting power induced by topological cavities is about 30 times that of the bare plate. Further studies on the effects of deliberately introduced defects on the output power show that the proposed energy harvesting system is highly robust against symmetry-preserving defects, and is less influenced even for symmetry-breaking defects at moderate perturbation level. Beyond the reported energy harvesting application, we foresee that our work may open avenues for robust operations in the realm of wireless sensing and structural health monitoring.

Vortex solutions in nonpolynomial scalar QED

In order to investigate possible topological vortex structures in generalized models, we developed a perturbative generation approach for scalar-vector theories. We demonstrate explicitly that the dielectric permeability functions must have a nonpolynomial shape, i. e., the form of the logarithmic function. Basing on this result, we built models in $(2+1)D$ with logarithmic dielectric permeability in order to investigate the presence of topological vortex structures in a Maxwell model. This type of scalar-vector models is important because they can generate stationary field solutions in theories describing the dynamics of the scalar field. As examples, we chose models of the complex scalar field coupled to the Maxwell field. Subsequently, we investigated the model's Bogomol'nyi equations to describe the field configurations. Then, we demonstrate numerically, for an ansatz with rotational symmetry, that the solutions of the complex scalar field generating minimum energy configurations are topological structures depending on the parameters obtained in the perturbative generation of the vector-scalar theory.

Vortex-line topology in iron-based superconductors with and without second-order topology

The band topology of a superconductor is known to have profound impact on the existence of Majorana zero modes in vortices. As iron-based superconductors with band inversion and $s_{\pm}$-wave pairing can give rise to time-reversal invariant second-order topological superconductivity, manifested by the presence of helical Majorana hinge states in three dimensions, we are motivated to investigate the interplay between the second-order topology and the vortex lines in both weak- and strong-Zeeman-field regimes. In the weak-Zeeman-field regime, we find that vortex lines far away from the hinges are topologically nontrivial in the weakly doped regime, regardless of whether the second-order topology is present or not. However, when the superconductor falls into the second-order topological phase and a topological vortex line is moved close to the helical Majorana hinge states, we find that their hybridization will trivialize the vortex line and transfer robust Majorana zero modes to the hinges. Furthermore, when the Zeeman field is large enough, we find that the helical Majorana hinge states are changed into chiral Majorana hinge modes and thus a chiral second-order topological superconducting phase is realized. In this regime, the vortex lines are always topologically trivial, no matter how far away they are from the chiral Majorana hinge modes. By incorporating a realistic assumption of inhomogeneous superconductivity, our findings can explain the recent experimental observation of the peculiar coexistence and evolution of topologically nontrivial and trivial vortex lines in iron-based superconductors.

Topological vortices for sound and light.

Localized zero-energy fermionic states can bind to topological defects such as two-dimensional vortices, which can be realized in the bulk of artificial acoustic and optical lattices.

Meron, skyrmion, and vortex crystals in centrosymmetric tetragonal magnets

The recent experimental confirmation of a transformation between meron and skyrmion topological spin textures in the chiral magnet Co$_8$Zn$_9$Mn$_3$ [S.-Z. Lin et al., Phys. Rev. B 91, 224407 (2015); X. Z. Yu et al., Nature 564, 95 (2018)] confirms that the skyrmion crystals discovered in 2009 [S. M\"{u}hlbauer et al., Science 323, 915 (2009)] are just the tip of the iceberg. Crystals of topological textures, including skyrmions, merons, vortices, and monopoles, can be stabilized by combining simple physical ingredients, such as lattice symmetry, frustration, and spin anisotropy. The current challenge is to find the combinations of these ingredients that produce specific topological spin textures. Here we report a simple mechanism for the stabilization of meron, skyrmion, and vortex crystals in centrosymmetric tetragonal magnets. In particular, the meron/skyrmion crystals can form even in absence of magnetic field. The application of magnetic field leads to a rich variety of topological spin textures that survive in the long wavelength limit of the theory. When conduction electrons are coupled to the spins, these topological spin textures twist the electronic wave functions to induce Chern insulators and Weyl semimetals for specific band filling fractions.

Investigation of Flow Separation Characteristics in a Pump as Turbines Impeller Under the Best Efficiency Point Condition

Abstract The impeller, which is the main energy conversion component of a pump as turbine (PAT), is designed for pumping mode, and its internal flow characteristics are quite complicated even at the best efficiency point (BEP) of the turbine mode. This study aims to investigate the flow separation characteristics in a PAT impeller under the BEP condition by numerical method. The hydraulic performance and transient pressure characteristics of PAT predicted numerically were verified through experimentation. The surface friction lines and flow topological structure were applied to diagnose the flow separation at the surface of the blade. The relationship between flow topological structure and vortex in the impeller and static pressure at the blade were analyzed. Analysis results show that the backflow and open flow separation are observed significantly in the leading region and near the shroud of the trailing region of suction side. The passage vortex always appears near the spiral node. The saddle point and spiral node correspond to the peak position of adverse pressure and the lowest position between two peak values of the static pressure of the blade, respectively. The inflow conditions of blade and shape of the trailing edge significantly influence the flow separations in the impeller.

Fractional Charge States in the Magneto-Photoluminescence Spectra of Single-Electron InP/GaInP2 Quantum Dots.

We used photoluminescence spectra of single electron quasi-two-dimensional InP/GaInP2 islands having Wigner-Seitz radius ~4 to measure the magnetic-field dispersion of the lowest s, p, and d single-particle states in the range 0–10 T. The measured dispersion revealed up to a nine-fold reduction of the cyclotron frequency, indicating the formation of nano-superconducting anyon or magneto-electron (em) states, in which the corresponding number of magnetic-flux-quanta vortexes and fractional charge were self-generated. We observed a linear increase in the number of vortexes versus the island size, which corresponded to a critical vortex radius equal to the Bohr radius and closed-packed topological vortex arrangements. Our observation explains the microscopic mechanism of vortex attachment in composite fermion theory of the fractional quantum Hall effect, allows its description in terms of self-localization of ems and represents progress towards the goal of engineering anyon properties for fault-tolerant topological quantum gates.

Visualization of large-scale charged domain Walls in hexagonal manganites

A ferroelectric charged domain wall (CDW) carries bound charges, originating from the variation of the normal components of polarization across the domain boundary, leading to a possible two-dimensional conductive interface in insulating materials. The ferroelectric CDW can be precisely created, erased, and manipulated, therefore offering an intriguing pathway toward the design of nano-devices. However, due to rather large energy costs, the size of the CDW is usually on the nanoscale. Here, taking flux-grown ferroelectric hexagonal manganites (h-RMnO3) as an example, we creatively adopted an accessible inclined polishing process to reveal the domain evolution of stripe, loop, and vortex domain patterns by depth profiling. Interestingly, we observed an unexpected large-scale straight CDW in as-grown LuMnO3 with length up to a millimeter size, which may result from the “polar catastrophe” during the flux growth. The large-scale CDW has a residual influence on the formation of the loop domain when the crystal anneals below the ferroelectric transition temperature, but completely disappears as the topological vortices emerge. The observed large-scale CDWs make h-RMnO3 a potential candidate for advanced electronic devices, leading to a panoply of desired properties.

Unconventional U(1) to Zq crossover in quantum and classical q -state clock models

We consider two-dimensional $q$-state quantum clock models with quantum fluctuations connecting states with clock transitions with different choices for matrix elements. We study the quantum phase transitions in these models using quantum Monte Carlo simulations, with the aim of characterizing the cross-over from emergent U(1) symmetry at the transition (for $q \ge 4$) to $Z_q$ symmetry of the ordered state. We also study classical three-dimensional clock models with spatial anisotropy corresponding to the space-time anisotropy of the quantum systems. The U(1) to ${Z_q}$ symmetry cross-over in all these systems is governed by a dangerously irrelevant operator. We specifically study $q=5$ and $q=6$ models with different forms of the quantum fluctuations and different anisotropies in the classical models. We find the expected classical XY critical exponents and scaling dimensions $y_q$ of the clock fields. However, the initial weak violation of the U(1) symmetry in the ordered phase, characterized by a $Z_q$ symmetric order parameter $\phi_q$, scales in an unexpected way. As a function of the system size $L$, close to the critical temperature $\phi_q \propto L^p$, where the known value of the exponent is $p=2$ in the classical isotropic clock model. In contrast, for strongly anisotropic classical models and the quantum models we find $p=3$. For weakly anisotropic classical models we observe a cross-over from $p=2$ to $p=3$ scaling. The exponent $p$ directly impacts the exponent $\nu'$ governing the divergence of the U(1) to $Z_q$ cross-over length scale $\xi'$ in the thermodynamic limit, according to the relationship $\nu'=\nu(1+|y_q|/p)$, where $\nu$ is the conventional correlation length exponent. We present a phenomenological argument based on an anomalous renormalization of the clock field in the presence of anisotropy, possibly as a consequence of topological (vortex) line defects.

Introduction of the vortex Hermite-Cosh-Gaussian beam and the analysis of its intensity pattern upon propagation

In this paper, a vortex-Hermite-cosh-Gaussian beam (vHChGB) is introduced as a general form of the vortex cosh-Gaussian and vortex Hermite-Gaussian beams. Based on the Huygens-Fresnel diffraction integral, a propagation formula of the vHChGB passing through a paraxial optical system is derived. The evolution of the intensity pattern of the propagated vHChGB as a function of the beam order, decentered parameter (b parameter) and topological vortex charge is discussed with numerical results. It is shown that the vHChGB shape in the source plane depends crucially on the decentered parameter. In far-field, the multi-lobe profile obtained for small b evolves into a four-petal-like beam. Whereas the initial four-lobe profile for large b, morphs into a multi-lobes pattern. The vHChGB shows specific intensity patterns depending on the beam order and the vortex charge. This study may be beneficial for applications involving beam shaping of hollow vortex beam, beam splitting techniques and optical communications.

Monte Carlo study on domain wall dynamics of J1–J2 triangular spin system

Monte Carlo simulations are employed to study the model of a triangular Ising antiferromagnet with the next-nearest neighbor ferromagnetic interaction (TIAFF), which can be well mapped to a six-state clock model, and provide a new model to explore the excitation of a topological six-state domain vortex. The TIAFF model retains the symmetry of the lattice and provides more details of vortex excitations and micro dynamics. The crossover of the domain walls in three sub-lattices creates the topological six-state domain vortices. The attractive force between the vortex and the anti-vortex is proportional to the number of domain walls that connect them. The movement of the vortex in the lattice is along the domain walls to avoid creating new defects. Our simulation works reveal that vortices obeying Arrhenius law are difficult to excite at a low temperature. Therefore, the surviving vortices are generated through the Kibble–Zurek mechanism (KZM), which explains the formation of topological solitons in a nonequilibrium system. The existing vortices in the system go through a slow random walk and annihilate in the first-order kinetic process.

Crystals of Topological Vortices in Compact Electrodynamics

This study concerns the changes in the topological properties of four-dimensional compact lattice electrodynamics. The requirement of model compactness leads to the appearance of topological defects (monopoles) creating magnetic currents. Available calculations demonstrate the occurrence of a phase transition for the birth of monopoles. In this work, a phase transition between various states has been revealed inside this phase along with some indications to the possibility of a single “monopole” phase to separate into smaller ones, which differ in the order of the arrangement of magnetic currents and their intensity. The regularity of this consideration and the consequences confirming the presence of a second phase transition in the model are substantiated. The dependence of the correlation properties of magnetic currents on the direction is demonstrated. A new method that comprehensively illustrates the changes in currents in different states with the use of geometric construction is proposed for the analysis of phase transitions.

Higgs-confinement phase transitions with fundamental representation matter

We discuss the conditions under which Higgs and confining regimes in gauge theories with fundamental representation matter fields can be sharply distinguished. It is widely believed that these regimes are smoothly connected unless they are distinguished by the realization of global symmetries. However, we show that when a $U(1)$ global symmetry is spontaneously broken in \emph{both} the confining and Higgs regimes, the two phases can be separated by a phase boundary. The phase transition between the two regimes may be detected by a novel topological vortex order parameter. We first illustrate these ideas by explicit calculations in gauge theories in three spacetime dimensions. Then we show how our analysis generalizes to four dimensions, where it implies that nuclear matter and quark matter are sharply distinct phases of QCD with an approximate $SU(3)$ flavor symmetry.

Bulk and surface topological indices for a skyrmion string: current-driven dynamics of skyrmion string in stepped samples

The magnetic skyrmion is a topological magnetic vortex, and its topological nature is characterized by an index called skyrmion number which is a mapping of the magnetic moments defined on a two-dimensional space to a unit sphere. In three-dimensions, a skyrmion, i.e., a vortex penetrating though the magnet naturally forms a string, which terminates at the surfaces of the magnet or in the bulk. For such a string, the topological indices, which control its topological stability are less trivial. Here, we study theoretically, in terms of numerical simulation, the dynamics of current-driven motion of a skyrmion string in a film sample with the step edges on the surface. In particular, skyrmion–antiskyrmion pair is generated by driving a skyrmion string through the side step with an enough height. We find that the topological indices relevant to the stability are the followings; (1) skyrmion number along the developed surface, and (2) the monopole charge in the bulk defined as the integral over the surface enclosing a singular magnetic configuration. As long as the magnetic configuration is slowly varying, the former is conserved while its changes is associated with nonzero monopole charge. The skyrmion number and the monoplole charge offer a coherent understanding of the stability of the topological magnetic texture and the nontrivial dynamics of skyrmion strings.

Double Majorana vortex zero modes in superconducting topological crystalline insulators with surface rotation anomaly

The interplay of time-reversal and $n$-fold rotation symmetries ($n=2,4,6$) is known to bring a new class of topological crystalline insulators (TCIs) having $n$ surface Dirac cones due to surface rotation anomaly. We show that the proximity-induced $s$-wave superconductivity on the surface of these TCIs yields a topological superconducting phase in which two Majorana zero modes are bound to a vortex, and that $n$-fold rotation symmetry ($n=2,4,6$) enriches the topological classification of a superconducting vortex from $\mathbb{Z}_2$ to $\mathbb{Z}_2\times\mathbb{Z}_2$. Using a model of a three-dimensional high-spin topological insulator with $s$-wave superconductivity and two-fold rotation symmetry, we show that, with increasing chemical potential, the number of Majorana zero modes at one end of a vortex changes as $2\to1\to0$ through two topological vortex phase transitions. In addition, we show that additional magnetic-mirror symmetry further enhances the topological classification to $\mathbb{Z} \times \mathbb{Z}$

Magnetic field-induced vortex triplet and vortex lattice in a liquid crystal cell

ANID-Millennium Science Initiative Program ICN17_012 Comision Nacional de Investigacion Cientifica y Tecnologica (CONICYT) CONICYT FONDECYT 1180903

Patterns of vortex generation behind a cylinder in a wall-bounded cross-flow during transition to turbulence

The paper elaborates on experimental investigation and direct numerical simulation of the wake flow behind a circular cylinder located near the wall of a rectangular channel. The study considers the Reynolds number range that covers transition to turbulence in the wake. Spiral fluid motion directed from the sidewalls to the channel center is revealed behind the cylinder for both positions of the cylinder considered in the study. The paper describes the effect of this motion on the critical Reynolds number corresponding to the onset of Karman vortex street and on the vortex topology. The spiral motion is shown to correlate with the onset of low-pressure regions behind the cylinder near the sidewalls. These regions result from the interaction between the boundary layer on the sidewalls and the separation region behind the cylinder.

Vortex structures in photodetachment by few-cycle circularly polarized pulses

Generation of electron vortices in photodetachment of ${\mathrm{H}}^{\ensuremath{-}}$ by circularly polarized laser pulses is analyzed by means of strong-field approximation and by numerically solving the time-dependent Schr\"odinger equation. A very good agreement is shown for the magnitude and the phase of the probability amplitude of photodetachment from both approaches. We demonstrate that spiral-like patterns in the probability amplitude of detachment, observed for a pair of counter-rotating circularly polarized laser pulses, cannot be associated with nonvanishing topological charge vortices. The latter can be generated, on the other hand, by a circularly polarized laser pulse or a sequence of such pulses with corotating polarizations. Such interpretation of our results follows from the hydrodynamical formulation of quantum mechanics and its generalization to arbitrary parametric spaces.